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

Answer:

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

$\frac{1}{33}$ = work rate of inlet pipe

$\frac{1}{34}$ = work rate of drain pipe

Using the formulae

Volume of flow=work rate $\times$ time

Let us assume complete time of pool to fill = 1

Remaining fraction of pool to be filled = $1-\frac{1}{3}=\frac{2}{3}$

$\begin{array}{l}{\frac{1}{33} x-\frac{1}{34} x=\frac{2}{3}} \\\\ {\frac{x}{33}-\frac{x}{34}=\frac{2}{3}}\end{array}$

$\frac{34 x-33 x}{33 \times 34}=\frac{2}{3}$

$34 x-33 x=\frac{2 \times 34 \times 33}{3}$

$\begin{array}{l}{x=\frac{2244}{3}} \\\\ {x=\frac{3168}{3}} \\\\ {x=748}\end{array}$

Time it will take to fill the pool = 748 hrs