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	Water is being pumped into the pool		2006-10-24
		From Jon: A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end. a) what percent of the pool is filled? b) at what rate is the water level rising? Answered by Stephen La Rocque.
	How fast is the water level rising		2006-08-12
		From Erin: Water runs into a conical tank at the rate of 9ft3/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r2 h). Answered by Penny Nom.
	Related rates and an oil spill		2006-02-12
		From Brandon: An Oil Tanker Spills 100,000 cubic meters of oil, which forms a slick that spreads on the water surface in a shape best modeled by a circular disc is increasing at a rate of 3m/min (it doesn't state what is increasing at 3m/min, so I'm assuming Radius until I can ask my teacher.) At t=T, the area of the "circular" slick reaches 100pi Sq. meters. A) how fast is the area of the slick increasing at t=T B)How fast is the thickness of the slick decreasing at t=T C)Find the rate of change of the area of the slick with respect to the thickness at t=T. Answered by Penny Nom.
	Two related rates problems		2005-12-29
		From Shimaera: #1. A manufacturer determines that the cost of producing x of an item is C(x)=0.015x2+12x+1000 and the price function is p(x)=250+2x/10. Find the actual and marginal profits when 500 items are produced. #2. At 9 a.m a car is 10km directly east of Marytown and is traveling north at 100 km/h. At the same time, a truck leaves Marytown traveling east at 70 km/h. At 10 a.m, how is the distance between the car and the truck changing? Answered by Penny Nom.
	One car leaves a spot traveling at 100 km per hour		2005-12-28
		From Jason: One car leaves a spot traveling at 100 km per hour. The second car leaves the same spot 15 minutes later and traveling at 120 km per hour. How long does it take for the second car to catch up to the first car? Answered by Penny Nom.
	A point is moving on the graph of x^3 + y^2 = 1 in such a way that		2005-09-17
		From Gina: A point is moving on the graph of x3 + y2 = 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second. Answered by Penny Nom.
	At what rate is the circumference of the circle increasing?		2005-08-08
		From John: A mathematics professor is knitting a sweater. The main part of the sweater is knit in a large spiral, ending up with a diameter of 30 inches. She knits at a constant rate of 6/7 square inches per minute. 1. At what rate is the circumference of the circle increasing when the diameter is 2 inches? 2. How long will it take her to finish this piece of the sweater? Answered by Penny Nom.
	A lighthouse is located on a small island,...		2005-07-14
		From Brittnee: A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom.
	Related rates and baseball		2004-04-26
		From Bethany: A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing? Answered by Penny Nom.
	A changing rectangle		2004-04-03
		From A student: The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? Answered by Penny Nom.
	Some calculus problems		2004-04-01
		From Weisu: I have questions about three word problems and one regular problem, all dealing with derivatives. Find all points on xy=exy where the tangent line is horizontal. The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15? A car and a truck leave the same intersection, the truck heading north at 60 mph and the car heading west at 55 mph. At what rate is the distance between the car and the truck changing when the car and the truck are 30 miles and 40 miles from the intersection, respectively? The production P of a company satisfies the equation P=x2 + 0.1xy + y2, where x and y are the inputs. At a certain period x=10 units and y=8 units. Estimate the change in y that should be made to set up a decrease of 0.5 in the input x so that the production remains the same. If you could just give me some hints on these questions, I'd really appreciate it. Thanks! Answered by Penny Nom.
	A pyramid-shaped tank		2004-02-13
		From Annette: The base of a pyramid-shaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston.
	Related rates		2002-04-17
		From Molly: A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared? Answered by Penny Nom.
	A lighthouse and related rates		2001-11-29
		From Melissa: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom.
	Related Rates		2000-05-07
		From Derek: How can you show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate. Answered by Harley Weston.

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