Question

An inlet pipe on a swimming pool can be used to fill the pool in 20 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

We have the next given information:

- inlet pipe fill rate = 1/20 = 1job/hour

-The drain pipe empty rate = 1/45 job/hour

- The pool is 1/3 filled, then we need to fill 2/3.

If both are open, we have the next combined rate:

Combined rate =1/20 - 1/45 = 25/(20*45) = 25/900=1/36 = 1job/hour

Now,we need yo use the next equation:

rate * time = work done

Set x for time.

Replacing:

1/36 * x = 2/3

Multiply both sides by 36:

$\begin{gathered} \frac{1}{36}*x=\frac{2}{3} \\ 36\left(\frac{1}{36}\right?x=36\ast\frac{2}{3} \\ x=24 \end{gathered}$

Hence, it will take 24 hours to fill the pool