Question

An inlet pipe on a swimming pool can be used to fill the pool in 2020 hours. The drain pipe can be used to empty the pool in 2121 hours. If the pool is 2323 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool

Answer 1

If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool

Explanation:

An inlet pipe can fill the pool in hours = 20

Inlet pipe 1 hour work =
`(1)/(20)`

A drain pipe can empty the pool in 21 hours

Drain pipe 1 hour work =
`(1)/(21)`

Inlet pipe and drain pipe 1 hour together work =
`(1)/(20)-(1)/(21)=(1)/(420)`

Now we are given that the pool is 2/3 filled

So, remaining portion to be filled =
`1 - (2)/(3) = (1)/(3)`

So, Inlet pipe and drain pipe fill
`(1)/(420)` in hours = 1

So, they can fill 1/3 in hours =
`(1)/((1)/(420)) * (1)/(3) =140 hours`

Hence If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool