Respuesta :
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:
[tex]\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}[/tex]To find the time it will take to fill if the drain is left open, we have the equation:
[tex]\frac{1}{8}+(-\frac{1}{20})=\frac{1}{y}[/tex]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:
[tex]\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}[/tex]Cross multiply:
[tex]\begin{gathered} 3y=40(1) \\ \\ 3y=40 \end{gathered}[/tex]Divide both sides by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{40}{3} \\ \\ y=13.3hours\text{ = 13 hours }20\text{ minutes} \end{gathered}[/tex]Therefore, if the drain is left open, it will take 13.3 hours for the pipe to fill the pool.
ANSWER:
13.3 hours
