Question

One inlet can fill an empty pool in 8 hours and a drian can empty the pool in 20 hours. How long will It take the pipe to fill the pool if tbe drain is left open?___ hours

Answer 1

13 1/3 hours.

Step-by-step explanation:

First, we determine the rates of filling and draining the pool.

`\begin{gathered} \text{Rate of the inlet pipe}=(1)/(8) \\ \text{Rate of the outlet pipe}=(1)/(20) \end{gathered}`

Let x be the time taken to fill the pool by the inlet pipe if the drain is left open:

Therefore:

`(1)/(8)-(1)/(20)=(1)/(x)`

Next, solve for x:

Take the lowest common multiple of the left-hand side:

`\begin{gathered} (5-2)/(40)=(1)/(x) \\ (3)/(40)=(1)/(x) \\ x=(40)/(3) \\ x=13(1)/(3)\text{ hours} \end{gathered}`

It will take 13 1/3 hours to fill the pool.