 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Judith, a student: An old broken-down car 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? |
Hi Judith,
The key relationship her is that rate(speed) = distance/time. The units tell you this. The rate is in miles (distance) per hour (time) or miles/hour. You can use this relationship three times, once for the uphill part of the trip, a second time for the downhill part of the trip and a third time for the entire trip.
For the uphill section of the trip you know the distance (1 mile) and the rate (15 miles per hour) so you can use rate = distance/time to find the amount of time it takes to reach the top of the hill.
For the downhill section of the trip you know the distance (1 mile) but you don't know the rate or the amount of time it will take.
For the entire trip however you know the rate (30 miles per hour) and the distance (2 miles) so you can use rate = distance/time to determine the time required for the entire trip.
Thus you have the time required for the uphill portion and the time required for the entire trip. The difference is the time available for the downhill part of the trip. You also know the distance (1 mile) so you can find the average speed.
Sometime the result you get for this kind of problem is not what you expected.
Penny
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.