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?

Question

Mathematics

Dayanara

3 March, 11:05

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?

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Answers (1)

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Luis Bradley · Answer 1

22.5 hours

Step-by-step 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