SOLUTION: It takes 6 hours to fill a pool. It takes 8 hours to drain it. How long does it take to fill the pool if the drain is left opened when the pool is started to be filled?

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Let x = number of hours to fill the pool with both draining and filling.

1/6 = the part of the pool that can be filled in 1 hour
1/8= the part of the pool that can be drained in 1 hour

1/x= the part of the pool that is filled with both pipes open

1/6-1/8=1/x

Multiply both sides of the equation by 24x:


hours

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period.

So, working together, they can do



of the job in 1 time period.

Therefore, they can do the whole job in:



time periods.

All of that works nicely when people or things work together, but in the case of your problem, they are working against one another, so:

So, working against one another, they can do



of the job in 1 time period.

Therefore, they can do the whole job in:



time periods.

John