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

The volume of a rectangular prism is
V = L*w*h

Since L and w are constants, and h does only change as the water rises up, the rate of change of that volume by using the derivative is
dV/dt = L*w*dh/dt

Given dV/dt = 2.5 ft3/min, then
2.5 = 4*15*dh/dt
dh/dt = 1/24 ≈ 0.042 ft/min