How long would it take for pipe A to fill the pool?

Question

Pipe A can fill the pool within 6 hrs and Pipe B can drain it within 10 hrs. A staff opened the pipe B for 30 minutes and realized that the pool should not be drained so he turned it off and opened pipe A. 

Answer 1

Pipe B drains 1/10th of the pool's volume in an hour (in ten hours it would be done).

 

If it was opened for 30 minutes, assuming the pool was totally full to begin with, then it drained half of that amount. One tenth divided by two is 1/20th.

 

So Pipe B has drained 1/20th of the pool.

 

Pipe A fills 1/6th of the pool's volume in an hour. But it only needs to fill 1/20th of it back up. So our answer is going to be less than an hour.

 

What about half an hour? It would be a half of 1/6th, or 1/12th. Still too much.

 

We need some number x such that

 

1/6x = 1/20

 

We can now solve this equation for x.

 

Divide both sides by 1/6:

 

x = 6/20

 

So our answer is 6/20ths of an hour. A 10th of an hour is 6 minutes, so a 20th of an hour is half that: 3 minutes.

 

6/20ths of an hour is then 6 * 3 minutes = 18 minutes.