Question

An inlet pipe on a swimming pool can be used to fill the pool in 14 hours. The drain pipe can be used to empty the pool in 21 hours. If the pool is 1/2 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

The inlet pipe can fill the pool in 14 hours and the drain can empty the pool in 21 hours.

Initially, the pool is 1/2 filled. The inlet pipe can fill the rest in 7 hours and the drain pipe can empty it in 21/2 = 10.5 hours.

In one hour, the inlet pipe fills 1/7 of the remaining fillable volume. The drain pipe can empty 1/10.5 of the volume.

This means that in one hour, the real input is:

$\frac{1}{7}-\frac{1}{10.5}=\frac{1}{21}$

This means that when both pipes are acting together, the pool will fill in 21 hours.