Question

An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 14 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.

Answer 1

It would take 270 more hours to fill the pool with both inlet and drain pipes open as the net rate after countering the drain pipe's effect is quite slow. By first finding the combined hourly rate and then dividing the remaining pool to fill by this net rate, we arrive at the total time required.

Step-by-step explanation:

To find out how many more hours it will take to fill the swimming pool with both the inlet pipe and drain pipe open, we need to understand the concept of rates. The inlet pipe fills the pool at a rate of 1/40 pools per hour (since it can fill the pool in 40 hours), and the drain pipe empties it at a rate of 1/45 pools per hour.

First, let's calculate the combined rate when both pipes are working together. We subtract the draining rate from the filling rate:

Filling rate - Draining rate = Net rate

1/40 - 1/45 = (45 - 40) / (40 * 45) = 5 / 1800 = 1 / 360 pools per hour

Since the pool is already 1/4 filled, we need to fill the remaining 3/4 of the pool. Now, we calculate the time required to fill the remaining pool at the net rate:

Time = Pool to fill / Net rate

Time = (3/4) / (1/360) = 3/4 * 360/1 = 270 hours to fill the remaining 3/4 of the pool.

Answer 2

It would take 90 hours to fill the pool.

Step-by-step explanation:

There is a mistake in the question so it is corrected below:

An inlet pipe on a swimming pool can be used to fill the pool in 40 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool?

Now, to find the hours would it take to fill the 1/4 pool.

Let the hours it take to fill the
`(1)/(4)` pool be
`h.`

A swimming pool can be used to fill the pool in 40 hours.

So, the rate of filling the pool =
`(1)/(40)` .

As, given the drain pipe can be used to empty the pool in 45 hours.

Thus, the rate of draining the pool =
`(1)/(45)` .

According to question:

`(1)/(40) -(1)/(45) =((1)/(4))/(h)`

`(1)/(40) -(1)/(45) =(1)/(4h)`

`(45-40)/(1800) =(1)/(4h)`

`(5)/(1800) =(1)/(4h)`

Using cross multiplication:

`20h=1800`

Dividing both sides by 20 we get:

`h=90\ hours.`

Therefore, it would take 90 hours to fill the pool.