Question

One inlet pipe can fill an empty pool in 8 hours, and a drain can empty the pool in 20 hours. How long will it take the pipe to fill the pool if the drain is left open?_____ hours

Answer 1

Given:

Time it takes the pipe to fill the pool = 8 hours

Time it takes to drain the pool = 20 hours

Let's find the time it will take the pipe to fill the pool if the drain is left open.

We have the rates as:

$\begin{gathered} \text{ }Rate\text{ to fill the pool = }\frac{1}{8}of\text{ the pool per hour} \\ \\ \text{ Rate to drain the pool = -}\frac{1}{20\text{ }}\text{ of the pool per hour} \end{gathered}$

To find the time it will take to fill if the drain is left open, we have the equation:

$\frac{1}{8}+(-\frac{1}{20})=\frac{1}{y}$

Where y represents the time it will take to fill the pool if the drain is left open.

Let's solve for y.

We have:

$\begin{gathered} \frac{1}{8}-\frac{1}{20}=\frac{1}{y} \\ \\ \frac{5(1)-2(1)}{40}=\frac{1}{y} \\ \\ \frac{5-2}{40}=\frac{1}{y} \\ \\ \frac{3}{40}=\frac{1}{y} \end{gathered}$

Cross multiply:

$\begin{gathered} 3y=40(1) \\ \\ 3y=40 \end{gathered}$

Divide both sides by 3:

$\begin{gathered} \frac{3y}{3}=\frac{40}{3} \\ \\ y=13.3hours\text{ = 13 hours }20\text{ minutes} \end{gathered}$

Therefore, if the drain is left open, it will take 13.3 hours for the pipe to fill the pool.

ANSWER:

13.3 hours