







Walking up and down a hill 
20140206 

From flo: michelle walks 4 km to the top of a hill at 3 km/h then immediately walks back down at an average speed of 5 km/h what is her average speed for the 8km walk Answered by Penny Nom. 





Why can't we add or subtract speed? 
20131121 

From kashish: why we cannot add or subtract "speed" / directly in any given distance , speed , time questions? Answered by Chris Fisher. 





One train overtaking another 
20131111 

From kiran: two trains of equal length are running in parallel tracks in the same direction with the speed of 60km/hr and 90km/hr respectively the latter completely crosses the former in 30 seconds the length of each train is in mtr Answered by Penny Nom. 





What is the original speed? 
20130810 

From MJ: If a truck increases its average speed by 10 km/h it can cover 60 km at the original speed in the same time that it can cover 80 km at the faster speed. What is the original speed? Answered by Penny Nom. 





6 miles in 28 minutes what's my average speed? 
20130305 

From lynda: 6 miles in 28 minutes what's my average speed? Answered by Penny Nom. 





Swimming upstream and downstream 
20130215 

From Kimberly: a beaver swims down to its lodge 4 times faster than it swims upstream. how many times faster is its speed in still water than the speed of the stream? Answered by Penny Nom. 





A journey of two parts 
20130206 

From Natalie: Mr Lim drove at 70 km per hour for 1 hour and 30 minutes. He then drove another 55 km. if his average speed for the whole journey was 80km per hour, what was his speed for the 55 km journey? Answered by Penny Nom. 





Revolutions per second 
20121018 

From Crystal: Suppose a car wheel is 26 inches in diameter.
a) If the tire completes one rotation, how far would the car travel?
b) If the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second? Answered by Penny Nom. 





Adding speeds 
20120826 

From Roy: May I ask if it is correct to add the following with units included? Some tell me that the units cannot be included in the addition because we cannot add speed. Answered by Harley Weston. 





A plane travelling with the wind and against the wind 
20120803 

From Gwen: The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed? Answered by Penny Nom. 





How fast am i driving? 
20120518 

From bozenga: How fast am I driving if I cover 40 feet in .1 seconds (1/10th of a second)? Answered by Penny Nom. 





How long will it take lee to catch up with jodie? 
20120321 

From kirsten: for example, if jodie is on the bus travelling at 10 m.p.h and lee is walking at 4 m.p.h how long will it take lee to catch up with jodie?? what is this mathematical name for this Answered by Harley Weston. 





Jack and Kate set off in their cars ... 
20120213 

From akiri: Jack and Kate set off in their cars from the same point to travel the same journey. Jack has a start of eight minutes before Katie sets off. If Jack travels at 50mph and Katie travels at 75mph, how many miles will be travelled when the two cars are level? Answered by Penny Nom. 





There is a police officer in pursuit of suspect 
20120201 

From Jay: There is a police officer in pursuit of suspect. They suspect is driving on a straight road traveling at 79 mph, the officer is 233 yds away, traveling at 92 mph, the suspects car 5 ft long and the officers car is 5.3 ft long, how long will it take to have the front of the officers car, equal to the front of the suspects car down to the tenth of a second. Answered by Harley Weston. 





Two trains passing each other 
20111207 

From Tamkeen: two trains 245m and 315m long are travelling toward each other at 90km/h and 54km/h respectively on parallel lines . how long do the train take to pass one another train the time they meet each other? Answered by Penny Nom. 





The average speed for the whole journey 
20111030 

From Shahzad: a train travels 68 Km at an average speed of 51Km/h. It then travels another 20Km at an average speed of 40Km/h before reaching its destination. Calculate the average speed for the whole journey? Answered by Penny Nom. 





37 miles in 3 seconds 
20111020 

From Joyce: Jake can travel 37 miles in 3 seconds,please calculate jake's rate of speed.(round to 2 decimal places) Answered by Penny Nom. 





What is the speed of the boat in still water? 
20111007 

From Hannah: The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water Answered by Penny Nom. 





Chuong and Hassan drive to work 
20111004 

From Dilshad: Chuong and Hassan both drive 40 km from home to work each day. One day Chuong said to Hasssan, "If you drive home at your usual speed, I will average 40 kmph faster than you and arrive home in 20 minutes less time." Find Hassan's speed. Answered by Penny Nom. 





Driving to meet Mary 
20110824 

From Denise: mary leaves St Paul traveling 2000 miles @ 55 MPH; John leaves LA traveling 2000 miles @ 45 MPH how many miles will John had traveled to meet mary? Answered by Penny Nom. 





Two boats 
20110329 

From Mamie: Two speed boats leave the port of San Francisco traveling in opposite directions
at the same time.One boat travels 8 knots per hour faster than the other.After
one day's travel they are 1,920 nautical miles apart.What are the speeds of the
two boats. Answered by Penny Nom. 





Average speed 
20110307 

From West: Calculate the distance (in km) that Larry runs if he maintains an average speed of 8km/hr for 45 minutes Answered by Penny Nom. 





What is its speed in miles per hour? 
20110106 

From Miriam: An airliner travels 125miles in 15minutes. What is its speed in miles per hour? Answered by Penny Nom. 





Angular speed 
20101212 

From Jason: 7 in. pulley traveling @ 175ft/sec. What is the rpm? Answered by Stephen La Rocque and Penny Nom. 





80 miles in 40 minutes 
20101208 

From james: i travel 8o miles in 40 minutes. how fast am i going in mph Answered by Penny Nom. 





Angular speed 
20101203 

From Julie: If the angular speed of a circle is 360 degrees divided by the time it took to rotate,
how do I calculate ones that have greater rotations than the amount of time?
I mean, you calculate the angular speed of a merrygoaround that spins once every 5 seconds
by doing 360degrees/5 sec, but how do you calculate a merrygoaround that has 16 rotations every 4 seconds? Answered by Penny Nom. 





What is its speed in still air? 
20101128 

From Shelby: An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x time Answered by Penny Nom. 





A train passes a car 
20101024 

From Mary: A train, whose speed is 75 mph, takes 3 minutes to pass a car that is going 60 mph in the same direction. How long is the train? Answered by Stephen La Rocque. 





What are the speeds of the boats? 
20101021 

From Adori: Two boats leave the port of San Francisco traveling in opposite directions at the same time. One boat travels 8 knots per hour faster than
the other. After one day's travel they are 1920 nautical miles apart. What are the speeds of the boats? Answered by Penny Nom. 





John and Mary are 200 miles apart 
20101020 

From Sarah: two people, john and mary, are 200 miles apart and leave at the same time to meet.
They are driving toward each other at constant rate on the same straight road.
John is traveling at 45 mph and Mary is traveling at 35 mph.
When they meet, how many miles will they be from john's house? Answered by Penny Nom. 





A commuter airline between two cities 
20101019 

From Adori: An airline runs a commuter between two cities that are 720 miles apart. If the average speed of the planes is increased by 40 miles per hour, the travel time is decreased An airline runs a commuter between two cities that are 720 miles apart. If the average speed of the planes is increased by 40 miles per hour, the travel time is decreased by 12 minutes. What airspeed is required to obtain this decrease in travel time? Answered by Penny Nom. 





Two jets leave denver at 9 am. 
20101015 

From Carl: two jets leave denver at 9 am. One flying east at a speed of 50 km per hour greater than the other which is traveling west. At 11 am the planes are 2500 km apart. Find their speeds. Answered by Stephen La Rocque. 





Two cars 
20100930 

From Amanda: Two cars, 142 miles apart, start moving towards each other at the same
time. One is moving 3 times as fast as the other. If they meet 1.7 hrs
later, find the average speed of the slower car in miles per hour? Answered by Penny Nom. 





What is the average speed? 
20100921 

From Cindy: A boat travels downstream m nautical miles at d knots. It travels upstream m nautical miles at u knots. What is the average speed for the entire trip? Answered by Penny Nom. 





Two cars on a circular track 
20100812 

From david: If two cars starts to drive at point 1 and go in a circle when will they meet?
(one cars speed is faster the other ) all I need is a formula Answered by Tyler Wood. 





How fast is the second car taveling? 
20100726 

From Jeff: A car is traveling 75 mph. It takes 12 miles to overtake a second car that was .5 mile ahead. How fast is the second car taveling? Answered by Stephen La Rocque. 





Pursuing Car 1 
20100713 

From Mark: Car 1 is traveling down the road at 50mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1? Answered by Robert Dawson. 





What is the speed of the current? 
20100525 

From tien: a boat travels upstream, against a current, at a speed of 4 miles per hour. On the return trip, the boat travels downstream, with the current , at 10 miles per hour. the speed of the current remains constant. what is the speed of the current? Answered by Penny Nom. 





When will the second truck catch up to the first? 
20100522 

From Josie: At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 45 mi/hr. At 11:00 a.m., a second truck leaves along the same route, travelling at 60 mi/hr. When will the second truck catch up to the first? Answered by Tyler Wood. 





Find the speed of the current of the river 
20100519 

From paul: a boat travels 100 miles downstream in the same length of time it travels 50 miles upstream. if the boat's speed in still water is 30 mph find the speed of the current of the river? Answered by Penny Nom. 





Sammy and his motorboat 
20100511 

From Jordan: Sammy owns a motorboat that travels 4 miles/hour in still water. It goes 12 miles upstream and 12 miles back again (downstream) in a total of 8 hours. Find the speed of the current of the river. Answered by Penny Nom. 





What is the speed of the current? 
20100317 

From Carl: If you can row 3 mph in still water and paddle 3 miles upstream and return in 3.6 hours then what is the speed of the current? Answered by Penny Nom. 





30.0 km per hour 
20100219 

From Diana: if a car travels 30.0 km per hour, how many km will it go in 2.0 hours? How far will it go in 15 minutes? Answered by Tyler Wood. 





How fast am I walking? 
20100110 

From KEVIN: IF I WALK 3 MILES IN 28 MINUTES, HOW FAST AM I WALKING? Answered by Penny Nom. 





e = m c^2 
20091209 

From Jim: Please explain the following formula:
E=MC2 (squared) Answered by Robert Dawson. 





... the original speed of the car was? 
20091208 

From venkatesh: A car travels a distance of 840 miles at a uniform speed if the speed of the car is increased 10 m/h more ,it takes two hours less to cover the same distance ,the original speed of the car was?
options:75 mh,65 m/h,60 m/h,55 m/h,45 m/h . Answered by Claude Tardif. 





Angular speed 
20091119 

From Atalie: The engine of a sports car rotates at 5000 revolution per minute. Calculate the angular speed of the engine in radians per second, given that 2pi radians = 1 revolution Answered by Robert Dawson. 





At what rate are the people moving apart? 
20091101 

From saira: A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ? Answered by Harley Weston. 





Two jets are traveling towards each other 
20091005 

From jake: two jets are traveling towards each other and are 4000 km apart. the rate of one jet is 100 km/h faster than the rate of the other. if the jets pass each other after 2.5 hrs what is the rate of speed of the faster jet? Answered by Penny Nom. 





How fast am i going? 
20090928 

From ron: how fast am i going if i drive 40 miles in 20 minutes...what is the formula for figuring this out. Answered by Leeanne Boehm. 





Average speed 
20090911 

From john: Sally travels by car from one city to another. She drives for 20.0 min at 68.0 km/h, 40.0 min at 37.0 km/h, and 51.0 min at 77.0 km/h, and she spends 12.0 min eating lunch and buying gas.
What is the average speed for the trip? Answered by Penny Nom. 





Average speed 
20090820 

From Christina: We ran 3.4 miles in 40 minutes. What was our average speed? Answered by Leeanne Boehm. 





Angular speed 
20090804 

From Mary: The engine of a sports car rotates at 5000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution. Answered by Penny Nom. 





Driving to school and back 
20090517 

From marylyne: suppose you are late for school and you drive from your house at a constant rate of 70 mph.when class is over, you drive home at a more leisurely 50mph. what is your average speed? Answered by Penny Nom. 





Two Boats 
20090516 

From Simon: Two boats, one travelling towards the east and the other travelling towards the north, are 10 km apart afetr an hour. If the speed of one boat is 2 more than the speed of the other boat, what is the speed of the faster boat? Answered by Stephen La Rocque. 





What was her rate of speed? 
20090506 

From Stephanie: beth paddled a canoe to a picnic spot in the river in 2 hours. she traveled up the stream back to the original spot in three hours. the current was two miles per hour.
What was her rate of speed? Answered by Robert Dawson and Stephen La Rocque. 





Two airplanes are 300 miles apart 
20090422 

From afzalsultan: Two airplanes are 300 miles apart and flying directly towards each other.One is flying at 200 miles per hour, and the other at 160 miles per hour.How long will it take for the two planes to meet Answered by Robert Dawson. 





Passing three cars 
20090416 

From Larry: If 3 cars are going 50 mph, and a fourth car pass the first 3 cars in 200 feet, how fast is the fourth car going? Answered by Stephen La Rocque. 





A man travels a total of 8km in 6 hours 
20090410 

From Kieran: Hello!
I was wondering if you could help me with this question! Thank you
A man travels a total of 8km in 6 hours
if his speed was xkm/4hours in the first stage
then his speed was 8x/2hours in the second part.
If the average speed for the first leg of the journey
was 1.1km/h faster than the second part: find x Answered by Penny Nom. 





How many miles per hour was it traveling? 
20090404 

From Regina: a car traveled 16 miles in 30 minutes. How many miles per hour was it traveling? Answered by Penny Nom. 





A trip at two different speeds 
20090328 

From A student: Good afternoon!
An automobile travels 4 hours at an average speed of 42MPH. How much
longer must the truck travel at an average speed of 55MPH so the
average speed for the total trip will be 50MPH?
Thank you for your assistance! Answered by Penny Nom. 





The speed of a tire in revolutions per minute 
20090328 

From Jules: Suppose that a tire on a car has an outer diameter of 2,5 feet. How many
revolutions per minute does that tire make when the car is travelling 60
miles per hour? (hint:first find the angular velocity in radians per minute.) Answered by Harley Weston. 





Fred in his canoe 
20090221 

From Susan: Fred paddled for 4 hours with a 7 km/hr current to reach a campsite. The return trip against the same current took 9 hr. Find the speed of Fred's canoe in still water. (Remember to include correct units) Answered by Penny Nom. 





Catching up to the car ahead 
20090206 

From Ashley: Car A passes Car B on a freeway. The driver of Car B decides to speed up to 75 mph and catch Car A, whose driver is maintaining a constant speed.
Looking ahead, the driver of Car B sees Car A go under an overpass oneqarter mile up the road. Exactly six minutes later, Car B catches Car A.
How fast was the car going? Answered by Penny Nom. 





A falling object 
20090201 

From Tamara: We drop an object from rest (i.e. its initial spped is zero. It is falling freely toward the ground. What will be its speed after 5 seconds of falling? Answered by Penny Nom. 





What will be its speed after 10s? 
20090201 

From Tamara: An object has an initial speed of 5 m/s and is accelerating with 2 m/s2 (m/s squared) acceleration. What will be its speed after 10s? Answered by Penny Nom. 





Linear speed 
20090126 

From Hom: A semi is driving cross country at 70mph. The tires on the semi have a 3 foot diameter. What is the linear speed in feet per minute? Answered by Robert Dawson. 





The speed of the boat and the river 
20081028 

From Jenn: On the Amazon River in Brazil, a boat goes 50 miles upstream in 3 hours, later the boat returns to the starting point in 2 hours. What is the speed of the boat in still water and what is the current speed in this part of the Amazon? Answered by Penny Nom. 





Finding the Speed of a Truck 
20080908 

From Rita: A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle theta between the highway and the line of observation from the patrol car to the truck is measured.
(a) If the angle measures 15 degrees, how fast is the truck traveling? Express the answer in feet per second and miles per hour. Answered by Janice Cotcher. 





Angular & Linear Speed from a Sine Graph 
20080819 

From Kim: Kim, a student:
I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer. Answered by Janice Cotcher. 





Running in opposite directions 
20080729 

From maame: if i run six miles per hour and my friend runs four miles per hour and we both run for two hours in opposite directions how many miles apart will we be after the two hours? Answered by Janice Cotcher and Penny Nom. 





Going to Neptune 
20080729 

From mariah: how fast would you be going per hour if you wanted to get to neptune in 1 week ? Answered by Penny Nom. 





Going from 45 mph to 35 mph 
20080709 

From Terry: How long (distance  feet AND time) will it take a car traveling at 45 mph to slow down to a speed of 35 mph? Answered by Harley Weston. 





Two trains 
20080707 

From Elisha: Trains at each end of the 50. km long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8. km/h faster than the train from England and they pass in 17 minutes. Answered by Janice Cotcher and Penny Nom. 





Miles per hour 
20080701 

From Nedra: If I walk 1 mile and 2/10ths in 20 minutes how fast am I going?
AND how many calories have I burned off? Answered by Penny Nom. 





The current in a river 
20080612 

From Joi: To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour. Answered by Harley Weston. 





Can the witness' statement be correct? 
20080602 

From Leria: The model S= radical 30df describes the relationship between the speed of a car , the conditions of the road, and the length of the skid marks when the car slams on the brakes. S is the speed of the car in miles per hour,
d is the length of the tires' skid marks in feet and f is the coefficient of the friction for the road.
In an accident, a car makes skid marks 85 feet long. The coefficient of friction is 0.6. A witness says that the driver was traveling faster than the speed limit of 35 miles per hour. Can the witness's statement be correct? Use algebra to explain your answer. Answered by Penny Nom. 





A cat is walking on the tread of a tank 
20080526 

From Kathleen: If a cat is walking on the tread of a tank travelling at 28kmh how fast does the cat have to walk to avoid falling under the tracks? Answered by Janice Cotcher. 





What is the altitude of the plane? 
20080423 

From tiana: If a plane is taking off and its climbing at 380 feet per minute at 205 MPH, what is the altitude of the plane after it traveled 115 miles? Answered by Penny Nom. 





A car is travelling at 80 km/hr speed 
20080410 

From mathew: A CAR TRAVELLING AT A SPEED OF 80km/hr. How much time will take this car to cross a tunnel of 100M Answered by Penny Nom. 





1 mile per minute 
20080401 

From jennifer: If you are traveling at 1 mile per minute how fast would you need to be going Answered by Stephen La Rocque. 





A train and a boat 
20080315 

From Sabrina: A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later? Answered by Harley Weston. 





Average speed up and down a hill 
20080309 

From Judith: An old brokendown ar has to travel a two miles route, up and down a hill.
Because it is so old, the car travels the first mile  the ascent  at an average
speed of fifteen miles per hour. How fast must it cover the second mile 
the decent  to achieve an average speed of thirty miles per hours?
(There is a missing variable, but what is it?) Answered by Penny Nom. 





A ball bearing is placed on an inclined plane 
20080215 

From Leah: A ball bearing is placed on an inclined plane and begins to roll.
The angle of elevation of the plane is x.
The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2.
What is the speed of the ball bearing,
and what value of x will produce the maximum speed at a particular time? Answered by Penny Nom. 





Radians 
20080208 

From Brian: I'm teaching Precalculus right now and will be covering the formula to convert angular speed into linear speed. My question is about the units involved. Using v=rw, if r is mearsured in feet and w is measured in radians/second then v is measured in ft/sec. What happened to the units of radians? I can't find a good way to explain why they are not part of units for velocity. Do you have a good explanation?
Thanks, Answered by Stephen La Rocque. 





Driving towards each other 
20080116 

From Shanda: Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 miles per hour faster than Charlene. They meet in 5 hours. Find Charlene's speed. Answered by Stephen La Rocque. 





What is the speed of the plane in still air? 
20080105 

From oscar: A plane flies 400 miles with the wind and 340 miles against the wind
in the same length of time. If the speed of the wind is 24mph, what is
the speed of the plane in still air? Answered by Penny Nom. 





How many complete revolutions does each wheel make? 
20071228 

From varoon: The wheels of a car are of diameter 80cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66kms per hour? Answered by Penny Nom. 





Two cars going in opposite directions 
20071125 

From alexa: two cars leave town at the same time going opposite directions. one of them
travels at 55 mph and the other at 65 mph. in how many hours will they be
150 miles apart? Answered by Penny Nom. 





Radial motion 
20071113 

From abdulai: a circular saw with diameter 18.4cm rotates at 2400rpm. What is the angular speed of a point on the edge of the saw blade in radians per second? Answered by Penny Nom. 





Stopping distance and speed 
20071111 

From Joanna: The algebraic relation d=0.0056^2 ++ 0.14s models the relation between a vehicle's stopping distance d, in metres, and its speed s, in kilometres per hour.
(a) What is the fastest you could drive and still be able to stop within 80 m?
(b) What is the stopping distance for a car travelling at 120 km/h?
(c) Estimate the length of an average car. How many car lengths does the the stopping distance in (b) correspond to? Answered by Stephen La Rocque. 





A car traveled 175m at certain speed 
20071028 

From abdi: A car traveled 175m at certain speed. if the speed had been 20 mph faster,
the trip could have been made in 1 hr less time. find the speed? Answered by Stephen La Rocque. 





Two cars 
20070917 

From Lanie: Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00am, each heading for Wildwood. One car's average speed is 10 miles per hour more than the other's. The faster car arrives at Wildwood at 11:00 am, 1/2 hour before the other car. What is the average speed of each car? How far did each travel? Answered by Stephen La Rocque. 





How many miles per hour was I driving 
20070911 

From Gary: How many miles per hour was I driving to go 37 miles in 13 minutes Answered by Victoria West. 





Speed of sunrise 
20070904 

From Robert: Facing west in a car, you are watching the sun rise (through the rear view mirror). It peaks the horizon, you take off driving. How fast would you have to drive, to see it rise again? Answered by Stephen La Rocque. 





Angular speed 
20070805 

From Virginia: the engine of a sports car rotates at 5,000 revolutions per minute (rpm). calculate the angular speed of the engine in radians per second. use 2n radians = 1 revolution Answered by Stephen La Rocque. 





A quarter of a mile in eight seconds 
20070629 

From Kevin: What speed is a vehicle traveling if he drove a quarter of a mile in eight seconds? Answered by Harley Weston. 





Average speeds 
20070622 

From Dee: A guy goes 3.1m a second for 29 seconds in a golf cart. He then walks 1.5 meters a second. How long does he have to walk to get the average speed of 2.1m a second? Answered by Stephen La Rocque. 





How fast was he going? 
20070603 

From Mary: if a motorcycle left a 63 foot skid mark before hitting a car how fast was he going ? Answered by Penny Nom. 





Converting speeds 
20070510 

From jason: A boy runs 36 metres in 6.50 seconds.How fast is he going in miles per hour Answered by Stephen La Rocque. 





A tugboat's speed 
20070430 

From Amanda: a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what
constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph. Answered by Stephen La Rocque. 





What is the speed of the boat? 
20070422 

From Sonja: A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed of the boat? The answer in the book says 14 mi/hr, but I don't understand how to figure it out. It must be very simple, but I'm stuck. Thank you so much for helping me out. This is a FANTASTIC website! Sonja Answered by Penny Nom. 





The second derivative 
20070414 

From Gerry: In mathematical context,what do you understand by the term "Second Derivative" Answered by Penny Nom. 





When will the rocket hit the ground? 
20070405 

From Megan: A model rocket is launched at an upward velocity of 460feet per second off a platform that is 40 feet up from the ground. Use the formula h(t)= 16+vo+ho where vo is the initial velocity an ho is the initial height.
A.) Find the maximum hight of the rocket.
B.) How long does it take to reach the maximum height?
C.) When will the rocket hit the ground? Answered by Stephen La Rocque. 





Velocity 
20070404 

From Jessica: The speed of the current in a river is 2mph. Jessica travels 20 miles upstream and then 20 miles downstream in a total time of 5 1/3 hr. Find the speed of the boat.
I know you have to use V= d/t, but what is the equation for time because you have to factor in that upstream the boat is slower and downstream the boat is faster? Answered by Penny Nom. 





A delivery driver travels from Belfast to an address in Dublin 
20070404 

From Gerry: A delivery driver travels from Belfast to an address in Dublin.The total distance fro the round trip
was x%.The time required for the forward trip was xx hours.Due to heavy traffic during the return trip an extra xx was required
How much slower was the delivery drivers speed on the return trip?.
I was wondering what equation would you use to solve this question. Answered by Penny Nom. 





Boat trigonometry 
20070404 

From Kimi: Hi,
I have been working on the attached math problem for my college trig class for over a week. Every avenue I've tried seems to lead either to a dead end, an unreasonable answer, or extremely complicated computations. I was able to calculate the speed of the boat to 3.51 mph, but cannot figure out the measure of angle beta. Once I can figure that out, I can do the rest of the problem.
Thanks,
Kimi Answered by Stephen La Rocque. 





Tina swims 4 miles upstream at 1 mph 
20070331 

From Michael: If Tina swims 4 miles upstream at 1 mph and back downstream to the same point to the same point at 4 mph, what is her average speed? Answered by Penny Nom. 





A beam on a lighthouse 
20070328 

From Lisa: A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P? Answered by Stephen La Rocque. 





Approximate average speeds 
20070319 

From Anne: A bicyclist pedaled up a 2 mile long hill averaging 4 miles per hour. Upon reaching the top, the bicyclist headed down a 6 mile descent averaging 26 mph. What was the bicyclist's approximate average speed?
Thanks very much in advance!! Answered by Stephen La Rocque and Penny Nom. 





How long does she have to get out of the way? 
20070223 

From Sharon: How do I solve this? The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s  16t^2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 6 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Answered by Penny Nom. 





Increasing speed and decreasing time 
20070218 

From Nigel: I am completely lost...can you help with this: The time, t, to travel a distance, d, at a constant speed, v, can be obtained from the formula: d = vt. If the speed is increased by x, find an expression to represent the decrease in time to travel the same distance. Answered by Stephen La Rocque. 





A gymnast is swinging on a high bar. 
20070214 

From William: A gymnast is swinging on a high bar. The distance between his waist (center of mass) and the bar is 1.1 m. If his speed at the top of his swing is zero and his gain in speed is due entirely to his change in gravitational potential energy, find his speed at the bottom of his swing. Answered by Stephen La Rocque. 





A person jumps from the roof of a house 
20070213 

From Jessie: A person jumps from the roof of a house 3.9m high. When he strikes the ground below, he bends his knees so that the torso decelerates over an approximate distance of 0.70m. If the mass of his torso (excluding legs) is 42kg, find a) his velocity just before his feet strike the ground , and b) the average force exerted on his torso by his legs during deceleration.
Please provide calculations and answers for comparison. Answered by Stephen La Rocque. 





Driving on a banked roadway 
20070205 

From William: A race track is shaped like an inverted cone. Race cars drive around this track in a horizontal path. If a drivers speed is 34 m/s, at what distance from the tip of the cone should he drive his car if there is no friction?
THANKS IN ADVANCE FOR ANY ASSISTANCE YOU CAN PROVIDE!
Sincerely, William Bush Answered by Stephen La Rocque. 





Freefalling objects 
20070125 

From Patricia: How long will it take a stone dropped from atop a 1000meter tall building to reach the ground? Answered by Stephen La Rocque. 





A college student jogs from his home to the beach 
20070123 

From Garmani: A college student jogs from his home to the beach at 8 miles per hour. He visits with his friends on the beach for 4 hours, and then his friends drive him home at the rate of 40 miles per hour. If the student returns home after 6 hour, what is the distance from his home to the beach? Answered by Penny Nom. 





What is the speed of each boat per hour? 
20070122 

From Garmani: Two tuna boats leave the same port traveling in opposite directions along the west coast of the United States. One boat travels 5 miles per hour faster than the other. At the end of one day's travel they are 1,080 miles apart. What is the speed of each boat per hour? Answered by Penny Nom. 





Angular speed 
20070118 

From Cristina: A car is moving at a rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet. a) Find the number of revolutions per minute the wheels are rotating. b) Find the angular speed of the wheels in radians per minute. Answered by Stephen La Rocque. 





At what speeds were they travelling? 
20070116 

From Maria: Kim and Julie are joining Nicole at her parents cottage for the weekend. The cottage is 150km away from their neighbourhood. Kim can leave directly after school but Julie will be leaving after band practice, an hour and a quarter later. Kim took her time and drove slowly, averaging 20km/h slower than Julie. They both arrived at the same time. At what speeds were they travelling? Answered by Stephen La Rocque. 





What is his rate of walking for the entire trip? 
20070112 

From Garmani: A man walks 500 feet at 4 miles per hour and returns to the starting point at 3 miles per hour. What is his rate of walking for the entire trip? Answered by Stephen La Rocque. 





Throwing a stone downwards 
20070112 

From Momo: a stone is thrown vertically downward with an initial speed of 14m/s from a height of 65 m above the ground. A) how far does the stone travel in the first 2.0 s? B) what is the stone velocity just before it hits the ground? Answered by Stephen La Rocque. 





What is the speed of the current? 
20070107 

From Bob: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? Answered by Haley Ess. 





Angular speed 
20070106 

From Robert: A rear wheel and tire on a John Deere 8520 farm tractor has a 39in. radius. Find the angle (in radians) through which a wheel rotates in 12 sec if the tractor is traveling at a speed of 22 mph. Answered by Penny Nom. 





The Metra and the Amtrack 
20061203 

From Amy: A Metra commuter train leaves Union Station in Chicago at 12 noon. Two hours later, an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3PM the Amtrak train is 10 miles behind the commuter train. How fast is each going? Answered by Stephen La Rocque and Penny Nom. 





A trip on the Grand River 
20061130 

From Kristy: Romo decided to make a 28km trip up and 28km trip down the Grand River. the speed of the current is 3km. one way Romo travelled with the current and the other way against the current. During his trip, Romo stopped for half an hour for lunch. if Romo's total trip lasted 6hours, how fast did he travel? Answered by Stephen La Rocque. 





How high is the satellite above the earth? 
20061113 

From Naomi: If the linear speed of a satellite in synchronous orbit is 1000 mi/h, how high is the satellite above the earth? Answered by Stephen La Rocque. 





Angular speed 
20061004 

From Jack: A horse on a merrygoround is 7m from the center and travels at a speed of 10km/h. What is its angular speed? Answered by Stephen La Rocque. 





How long will it be before the two snails meet? 
20060921 

From Brett: Two snails are 8.5 feet apart. They start to crawl toward each other at the same time. One of them travels at the speed of 6 in. per minute, while the other zips along at 11 inches per minute. How long will it be before the two snails meet? Answered by Penny Nom. 





Speed of a four wheeler 
20060814 

From Luke: My question is, i race four wheelers on weekends and was trying to find out how fast we are going i race 500 ft.in about 6.00 seconds .how do you figure out the speed i am traveling? Answered by Penny Nom. 





A point on a bicycle rim 
20060801 

From Sonu: Find the speed in m/s of a point on a bicycle rim of diameter 88cm making 200 revolutions per minute. Answered by Penny Nom. 





Flying with and against the wind 
20060706 

From Tim: When a plane flies with the wind, it travels 800 miles in 4 hours. Against the wind it takes 5 hours to cover the same distance. Find the rate of the plane in still air and the rate of the wind. Answered by Stephen La Rocque. 





A boat travels 60 miles upstream ... 
20060528 

From Teenarick: A boat travels 60 miles upstream against the current in 3 hours. It takes 2 hours for the return trip. Find the speed of the boat in still water. Answered by Penny Nom. 





An aircraft going from city A to city B 
20060510 

From Preston: An aircraft going from city A to city B on a bearing of S69 degrees East is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the plane's true bearing. Answered by Stephen La Rocque. 





How far from Earth is Neptune? 
20060321 

From Scott: A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune? Answered by Penny. 





Find the ground speed and the planes true heading. 
20060205 

From Jimmie: An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading. Answered by Penny Nom. 





Speed on a bicycle 
20050727 

From Deborah: We are trying to figure out how many miles per hour we rode in a bike race. If the distance was l5 miles and the time it took was was 55 minutes, what is the speed? Answered by Penny Nom. 





An aircraft is flying directly from airport A to airport B 
20041022 

From A student: In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i30j)km/h. Calculate
(i) the time of flight, to the nearest min
(ii) the direction of the wind. Answered by Penny Nom. 





Accelerating to the speed of light 
20040930 

From Lars: How long time would it take to accelerate up to the speed of light with an acceleration speed similar to 0100 seconds in 5 seconds? Answered by Penny Nom. 





The commuter 
20040714 

From JJ: A student who commutes 27 mi. to college remembers, after driving a few minutes, he forgot a term paper. Driving faster than usual, he returns home, gets the paper, and once again starts to school. Sketch the graph of the student's distance from home as a function of time.
Does it mean that the student drives at normal speed, drives faster to pick up the paper, and resumes normal speed to head back, or that the student drives at normal speed, then drives faster the rest of the way to college? Answered by Penny Nom. 





Angular speed 
20040201 

From Rachel: A 4 inch pulley on a motor makes 1500 revolutions/minute. It is connected to an 8 inch saw blade.
a. Find the angular speed of the pulley in radians/minute
b. Find the angular speed of the saw in radians/ minute
Answered by Harley Weston. 





The London marathon 
20040127 

From Nina: After a years training, Minnie Midriffe increased her average speed in the london marathon by 25%. By what percentage did her time decrease?o Answered by Penny Nom. 





What is the speed of the automobile? 
20040120 

From Rita: An automobile travels toward Nashville from Cookeville. It takes 33 minutes to travel from Cookeville to Manchester, which is a 36 mile distance. If the driver continues at this pace, what is the speed of the automobile? Answered by Penny Nom. 





A rock on a string 
20031026 

From A student: a rock on a 4' string is rotated at 80 rpm. what is the linear speed in feet per second? in miles per hour? Answered by Penny Nom. 





A boat travels 12 km upstream... 
20030903 

From Sohaib: A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3km/hr throughout, find the speed of the boat in still water, giving your answerĘcorrect to 3 decimal places. Answered by Penny Nom. 





A helicopter rises vertically 
20030902 

From Kate: A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)^{2} How far above the ground will the helicopter be after 3 seconds? Answered by Penny Nom. 





A radio controled car 
20030608 

From Robert: I have a radio controled car (scale size 1/43). This car can travel 490 ft. per minute. I would like to know how fast that is at that scale size in miles per hour (and Kilometers per hour)? Answered by Penny Nom. 





Two rate problems 
20020930 

From Rebecca:
 There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub?
 An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind?
Answered by Penny Nom. 





Flying with the wind 
20020519 

From SaraJean: It takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind. Find the air speed of the plane and the speed of the wind current. Answered by Penny Nom. 





A test drive 
20020423 

From Jennie: At 9 A.M. a test car driving at a constant speed passes a marker 50 miles from it's starting point. At noon the car is about 130 miles from the marker. If the test drive ends at 1:30 P.M., how far will the car be from its starting point? Answered by Penny Nom. 





Mr. Byrd's drive to work 
20020322 

From Mr. Bollen: Mr. Byrd leaves his house at 7:00am to go to work. If he drives 40 mph he will arrive 3 minutes late and if he drives 60mph he arrives 3 minutes early. At what speed will Mr. Byrd have to drive in order arrive exactly on time. Please describe how you arrived at your answer. Answered by Claude Tardif and Penny Nom. 





How far does the fly fly? 
20010807 

From Harold:
6 MPH 4 MPH
Rachel  Eli
10 Miles apart
The fly is on Rachels handlebars. The fly is scared so it flys back and forth at 20 MP H. How far has the fly flown when Rachel and Eli meet? f Answered by Penny Nom. 





The speed of the boat 
20010712 

From Sharon: A motor boat is travelling in a southeasterly direction in water that is flowing from the south at 2km per hour. Show that the speed of the boat is (6 times the square root of 2) km per hour, given that it can travel at 10km per hour in still water. Answered by Penny Nom. 





Average speed 
20010501 

From Tom: A ship goes in one direction, west to Hawaii, at 20 nautical miles per hour and, because of the wind, makes the return trip at 30 nautical miles per hour. What is the average speed? Answered by Claude Tardif. 





Processing speed 
20010126 

From Zac: A COMPUTOR IS ADVERTISED AS HAVING A PROCESSING SPEED OF 11 MILLION INSTRUCTIONS PER SECOND. ON THE AVERAGE, HOW LONG DOSE IT TAKE TO PROCESS ONE INSTRUCTION AT SUCH A SPEED? Answered by Leeanne Boehm. 





Cincinnati to WinstonSalem 
20010123 

From Belinda: Joan Bedney travels from Cincinnati to WinstonSalem at an average rate of 40 miles per hour and returns at an average rate of 60 miles per hour. What is her average speed for the trip? Answered by Leeanne Boehm and Claude Tardif. 





Gravity 
20000906 

From Robert Broomfield: If they dropped a 1lb object from 40,000 feet in the air, at what speed would it it the ground? Answered by Harley Weston. 





The speed of light 
20000619 

From Benny Lau: I have a personal questions. In physics,if a person is running on a train, his relative speed on the ground will be the addition of the speed of train and the person. If u have a train inside another train and inside another train, so on...... can u reach the speed of light? It would need a very long distance. But if we make all the train travel in circles. Then we don't need that much distance. So can we achieve the speed of Light? Answered by Robert Coleman and Harley Weston. 





Running Through a Train Tunnel 
20000401 

From Eugene Chan: A man is running through a train tunnel. When he is 2/3 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume he runs at a constant rate.) I think the answer (12 mph) is wrong. Also, I believe it should read 1/3 of the way through, but don't know how to prove it. Could you come up with some way to prove it, please? I would really appreciate it. Answered by Penny Nom. 





Word problems 
20000331 

From Amy: Question:  a north bound train left at noon. four hours later a south bound train left the same station. at 5 o'clook they were 160 miles apart. what was the rate of both if the north bound train was going 20 miles faster than the other one.
 clark's final exam was given 5 times the weight of the weight of a weekly test. the avgerage of 15 weekly test was 91. the overall weighted average was 85. what did he make on the final.
Answered by Penny Nom. 





Travelling from A to B 
20000320 

From Matt: A car is traveling from point A to point B. Point A and point B are 30 miles apart. A car travels 30 miles an hour from point A to point B and then goes back to point A. How fast does the car have to go back to average 60 miles an hour? Answered by Claude Tardif. 





A bike race 
19990423 

From Bill Gepford: Bill was in a bike race and his friend kyle calculated that if he went 15mph that he would cross the noontime checkpoint one hour early but if he rode 10mph he would arrive one hour late. How far away is the checkpoint? Answered by Penny Nom. 





Rowing on the Charles River. 
19970917 

From Fawwaz Muraisi: On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.How fast is the river flowing? Answered by Harley Weston. 

