Question

A trough is 15 ft long and 4 ft across the top. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft3/min. How fast is the water level rising when it is 0.89 ft deep? Give your answer correct to 3 decimal places.

Answer 1

when the water has depth y, the surface has with 4/3 y. That means the volume is

v = y(4/3 y)/2 * 15 = 10y^2
dv/dt = 20y dy/dt

Now just plug in your numbers to find dy/dt