Question

One hose can fill a small swimming pool in 90 minutes. A larger hose can fill the pool in 30 minutes. How long will it take the two hoses to fill the pool working together?

Answer 1

Working together they would fill two pools in 120 minutes so therefore they would fill one pool in 60 minutes

Answer 2

It will take 22.5 minutes the pool with the two hoses.

Explanation:

In this case we have to propose equations that could describe the filling of pool by the small and large hose, then sum them and find the time of fill with both:

Small hose:
`Volume=(Volume)/(90) *Time`

Large hose:
`Volume=(Volume)/(30) *Time`

Where Volumen is the total volume of the pool and Time is the total time of fill using the two hoses, now adding them:

`Volume=(Volume)/(90) *Time+(Volume)/(30) *Time`

We can clear the time:

`Volume=(3*Volume*Time+Volume*Time)/(90)`

`Volume=(4*Volume*Time)/(90)`

`Time=(90)/(4)`

`Time=22.5`

It will take 22.5 minutes the pool with the two hoses.