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Question 930780: A big pump can pump water out of a pool three times as fast as a small pump. If both pumps are going, they can empty out a pool in 4 hours. How long would it take the faster pump working alone?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=time it takes the small pump to empty the pool
Then small pump empties the pool at the rate of 1/x of the pool per hour
x/3=time it takes large pump to empty pool
Large pump empties the pool at the rate of (1/(x/3))=3/x of the pool per hour
Both pumps working together empties the pool at the rate of 1/4 of the pool per hour
Soooo 1/x + 3/x=1/4 multiply each term by 4x
4+12=x
x=16 hours ----time it takes small pump working alone to empty the pool
x/3=16/3=5 1/3 hours--time it takes large pump working alone to empty pool
CK
In 4 hours, small pump empties (1/16)*(4)=1/4 of the pool
In 4 hours, large pump empties (3/16)*(4)=3/4 of the pool
3/4 + 1/4=1 (one pool, that is)
In 5 1/3 = 16/3 hours, large pump empties (3/16)*(16/3)=1 (1 pool that is)
Hope this helps---ptaylor
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