Question

An inlet pipe on a swimming pool can be used to fill the pool in 38 hours. The drain pipe can be used to empty the pool in 42 hours. If2.the pool is filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your3answer to two decimal places, if needed.

Answer 1

`133\text{ hours}`

Step-by-step explanation:

Since the pool is 2/3 full before opening the inlet and draining pipes, the wor to be done here is to fill 1/3 of the pool.

We simply need to calculate the time it takes to fill 1/3 of the pool

Let the time be x hours

While the inlet pipe will be postively adding, the draining pipe would be taking away

Mathematically,we have it that:

`\begin{gathered} ((1)/(38)-(1)/(42))* x\text{ = }(1)/(3) \\ \\ x((42-38)/(38*42))\text{ = }(1)/(3) \\ \\ (12x)/(1596)\text{ = 1} \\ \\ 12x\text{ = 1596} \\ x\text{ = }(1596)/(12) \\ \\ x\text{ =133 hours} \end{gathered}`