Question

A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?

8 hours
12 hours
24 hours

Answer 1

12 hours..........
+ - = 1
Multiply by 12 to clear the fractions
3t + 2t - 4t = 12
t = 12 hrs to fill the pool

Answer 2

12 hours

Explanation:

Let t be time to fill with all pipes open

All the pipes will complete a single job that is = 1

Given is that the tank can be filled by one pipe in 4 hours and by a second pipe in 6 hours and can be drained by a third pipe in 3 hours.

So, equation forms;

`(t)/(4)+ (t)/(6)- (t)/(3)=1`

=>
`(3t+2t-4t)/(12) =1`

=>
`(t)/(12) =1`

And t = 12 hours

Hence, it will take 12 hours to do the job.