Question

An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. The drain pipe can be used to empty the pool in 34 hours. If the pool is 1/3 filled and than the inlet pipe and drain pipe are opened how long would it take to fill the pool

Answer 1

An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. Time it will take to fill the pool = 748 hrs

Solution:

Let x = time it will take to fill the pool

`(1)/(33)` = work rate of inlet pipe

`(1)/(34)` = work rate of drain pipe

Using the formulae

Volume of flow=work rate
`*` time

Let us assume complete time of pool to fill = 1

Remaining fraction of pool to be filled =
`1-(1)/(3)=(2)/(3)`

`\begin{array}{l}{(1)/(33) x-(1)/(34) x=(2)/(3)} \\\\ {(x)/(33)-(x)/(34)=(2)/(3)}\end{array}`

`(34 x-33 x)/(33 * 34)=(2)/(3)`

`34 x-33 x=(2 * 34 * 33)/(3)`

`\begin{array}{l}{x=(2244)/(3)} \\\\ {x=(3168)/(3)} \\\\ {x=748}\end{array}`

Time it will take to fill the pool = 748 hrs