SOLUTION: a new type of pump can drain a pool in 6 hours. an older pump can drain the pool in 12 hours. how long will it take both pumps working together to drain the pool?

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Question 1163560: a new type of pump can drain a pool in 6 hours. an older pump can drain the pool in 12 hours. how long will it take both pumps working together to drain the pool?
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, Alan3354:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!

Solve for x.
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Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

It can be solved mentally, without using equations.


The new pump works as productive as two old pumps.


So, the old pump and the new pump, working together, are equivalent to three old pumps.


One old pumps completes the job in 12 hours.   


Hence, the two pumps, been equivalent to 3 old pumps, will complete the job in 12/3 = 4 hours.      ANSWER

Solved.


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Another quick mental solution method -- very similar to, yet much different than, the one shown by tutor @ikleyn.

In 12 hours, the new pump could drain the pool 2 times -- or, more reasonably, it could drain 2 of the pools.
In the same 12 hours, the old pump can drain the pool once.
So together in 12 hours the two pumps could drain 3 of the pools.
And therefore the two together can drain the one pool in 12/3 = 4 hours.

That's the same logic as used in tutor @ikleyn's mental solution; but the thought process is a bit different.

Try both methods to see if one or the other "works" better for you.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
a new type of pump can drain a pool in 6 hours. an older pump can drain the pool in 12 hours. how long will it take both pumps working together to drain the pool?
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6*12/(6+12) = 4 hours
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For A hours and B hours ---> A*B/(A+B)
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