Chapter 11.5, Problem 23P

A pool has 2 pipes, one to fill it and one to empty it. Ms. Simon wants to fill the pool, but she mistakenly turns on both pipes at the same time. The pipe that fills the pool can fill it in 6 hours and the one that drains it can do that job in 10 hours. How Jong will it take to fill the pool now that both pipes are filling and emptying it at the same time?

To determine

To calculate the time taken to fill the tank completely.

Answer to Problem 23P

The time taken to fill the tank is $15$ hours.

Explanation of Solution

Given information:

The given statement is:

“A pool has two pipes, one to fill it and one to empty it. Ms. Simon wants to fill the pool but she mistakenly turns on both pipes at the same time. The pipe that fills the pool can fill it in $6$ hours and the one that drains it can do the job in $10$ hours. How long will it take to fill the pool now that both the pipes are filling and emptying it at the same time?”

Calculation:

Work done in filling the tank is $\frac{1}{6}$ .

Work done in emptying the tank is $\frac{1}{10}$ .

The work done together by the pipes can be calculated by:

  $\begin{array}{l}\frac{1}{6}-\frac{1}{10}\\ =\frac{5-3}{30}\\ =\frac{2}{30}\end{array}$

The time taken to fill the tank is:

  $\begin{array}{l}1÷\frac{2}{30}\\ =1\times \frac{30}{2}\\ =\frac{30}{2}\\ =15\end{array}$

Hence, the time taken to fill the tank is $15$ hours.