Question

An inlet pipe can fill a swimming pool in 9 hours and an outlet pipe can empty the pool in 12 hours. Through an error, both pipes are left open. How long will it take to fill te pool?

Answer 1

36 hours.

Explanation:

Let x represent time taken by both pipes to fill the tank.

We have been given that an inlet pipe can fill a swimming pool in 9 hours. So part of pool filled by inlet pipe in one hour would be
`(1)/(9)`.

We are also told that an outlet pipe can empty the pool in 12 hours. The part of pool emptied by outlet pipe in one hour would be
`(1)/(12)`.

Sine the time taken by both pipes to fill the tank is x hours, so part of pool filled by both pipes in one hour would be
`(1)/(x)`.

We will get an equation using our given information as:

`(1)/(x)=(1)/(9)-(1)/(12)`

Let us solve for x.

`(1)/(x)=(1*12)/(9*12)-(1*9)/(12*9)`

`(1)/(x)=(12)/(108)-(9)/(108)`

`(1)/(x)=(12-9)/(108)`

`(1)/(x)=(3)/(108)`

Cross multiply:

`3x=108`

`(3x)/(3)=(108)/(3)`

`x=36`

Therefore, it will take 36 hours for both pipes to fill the tank.