How long will it take to drain the pool once it is filled and only the drain valve is opened?

Question

Emmanuel was told that his pool will fill through an inlet valve in 12 hours. He knew something is wrong when the pool took 20 hours to fill. He found he had left the drain valve open. How long will it take to drain the pool once it is filled and only the drain valve is opened? Write a number sentence with the use of function notation and answer it.

Answer 1

1. assume the rate of filling and draining are constants
2. let the volume of the pool be V and Qi= rate of fill and Qo = rate of drain
3. note the V/12 = Qi and (Qi-Qo)*20=V
4. Solve for Qo to be V/60 = time to drain