Question

A swimming pool has 6 inlet pipes. Each pipe can
individually fill up the pool in 5 hours. There are 2
outlet pipes which can empty the pool in 10 hours
working individually. How long wit take to fill the
pool if all the pipes are opened skyltaneously.​

Answer 1

Add the rates of filling of the 2 filling pipes and

subtract the rate of draining of the emptying pipe

-------------

1st pipe's rate: ( 1 pool filled ) / ( 3 hrs )

2nd pipe's rate: ( 1 pool filled ) / ( 6 hrs )

-------------

3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 hrs )

-------------

Let t = the time in hrs to fill the pool with all 3 pipes open

1/3+1/6-1/4=1/t

Multiply both sides by 24t

8t+4t-6t=24

6t=24

t=4

It will take 4 hrs to fill the pool with all 3 pipes open