Question

A pond is being drained through an outlet pipe, then will be filled through an inlet pipe. If the inlet pipe can fill the pond in 9 hours and the outlet pipe can empty the pond in 15 hours, how long would it take to fill the pond if the outlet pipe was left open?

Answer 1

22.5 hours

Explanation:

I am using "1 pond" to mean the volume of water that fits in the pond.

The inlet pipe fills the pond in 9 hours.

The filling rate is (1 pond)/(9 hours) = 1/9 pond/hour

The outlet pipe empties the pond in 15 hours.

The emptying rate is (1 pond)/(15 hours) = 1/15 pond per hour

The difference in rates is the net rate at which the pond is filling up.

1/9 pond/hour - 1/15 pond/hour =

= 5/45 pond/hour - 3/45 pond /hour

= 2/45 pond/hour

The pond is filling at a rate of 2/45 pond/hour.

To find the time it takes to fill the pond, we divide 1 pond by the rate.

(1 pond)/(2/45 pond/hour) = 45/2 hour = 22.5 hours