Question

The san paulo community swimming pool can be filled in 12 hr if water enters through a pipe alone or in 30 hr if water enters through a hose alone. if water is entering through both the pipe and the hose, how long will it take to fill the pool?

Answer 1

Alright, lets gets started.

If water enters through a pipe alone, swimming pool can be filled in 12 hr.

Or say, in 12 hrs, swimming pool can be filled with help of pipe.

It means in 1 hr, the part of swimming pool filled =
`(1)/(12)` (For pipe only)

Similarly, with hose only, , in 1 hr, the part of swimming pool filled =
`(1)/(30)`

So, water is coming from both, pipe and hose , then in 1 hr, the part of pool filled will be =
`(1)/(12) + (1)/(30)`

Suppose in x hrs, with both supplies, pipe and hose, pool is filled.

Means

`(1)/(12) + (1)/(30) = (1)/(x)`

making common denominator

`(30)/(360) + (12)/(360) = (1)/(x)`

`(30 + 12)/(360) = (1)/(x)`

`(42)/(360) = (1)/(x)`

Flipping

`(360)/(42) = x`

`x = (60)/(7)`

Means 8.57 hrs : Answer

Hope it will help :)