David B.

asked • 02/13/18

Fill Pool with 2 hose

A swimming pool can be filled in 5 hours by hose A alone and 6 hours by hose B alone. How long would it take to fill the pool using both hoses?

Joel W.

Hose A fills the pool in 5 hours (1/5 per hour), hose B fills the pool in 6 hours (1/6 per hour)

In one hour the pool gets filled by 1/5 + 1/6 = 6/30 + 5/30 = 11/30
 
Pool volume is filled by 11/30 per hour, take the volume (30) and divide by how much it is filling per hour (11) to get the time.
 
30 / 11 = 2 8/11
 
It takes 2 8/11 hours to fill the pool, correct me if I'm wrong.
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02/13/18

1 Expert Answer

By:

Jeffrey K. answered • 08/17/20

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David, this is a common type of problem.


And the answer is NOT the average of 5 hours and 6 hours!


What we must do is find out how much of the pool each hose fills in 1 hour.

Clearly, the first hose fills 1/5 of the pool in 1 hour.

Similarly, the second hose fills 1/6 of the pool in 1 hour.


So, together, they fill 1/5 + 1/6 = 11/30 of the pool, in 1 hour.


What number must we multiply this fraction by in order to get 1, that is, the whole pool?

The answer, obviously, is the inverse of 11/30 = 30/11 (because 11/30 x 30/11 = 1)


So, the 2 hoses take 30/11 = 2 and 8/11 hours to fill the pool together.



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