How would I answer this derivative application question?

Question

Water is leaking from a trough at the rate of 0.8 L/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85cm, and the height is 25 cm. The length of the trough is 3 m. Find the rate at which the height is changing when the depth of water is 11 cm.

Answer 1

You need to express the volume as a function of time...and this means expressing the height as a function of time AND the upper base B as a function of time.

B as a function of h is linear: B=55+(6/5)h

Then volume as a function of time is 150[(6h/5)+110]h

Now differentiate V as a function of time (remember h is ALSO a function of time.

Plug in the values given for DV/dt and h and solve for dh/dt.