Question

It takes 12 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the outlet pipe. If the pool is 2 3 full to begin with, how long will it take to fill it from there if both pipes are open?

Answer 1

20 hour

Explanation:

Let the total capacity of the pool is 100%

It is given that 2/3 of the pool is already filled means
`100* (2)/(3)=66.66` % is already filled

So 100%-66.66%= 33.33 % pipe is empty

it is given that it takes 12 hours to fill the pool so inlet rate is
`(1)/(12)`

It is also given that it can empty in 15 hours so outlet rate is
`(1)/(15)` So equivalent rate for filling the pool is
`((1)/(12)-(1)/(15))* 100=1.666` %

So time required to fill the pool is
`=(33.33)/(1.666)=20` hour