SOLUTION: If a swimming pool can be filled in 15 hours by pipe A alone and in 24 hours by pipe B alone. How long would it take to fill the pool if both pipes were working?

Question 290206: If a swimming pool can be filled in 15 hours by pipe A alone and in 24 hours by pipe B alone. How long would it take to fill the pool if both pipes were working?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes if both pipes are working
Then both pipes fill at the rate of 1/x pool per hour
Pipe A fills at the rate of 1/15 pool per hour
Pipe B fills at the the rate of 1/24 pool per hour
Both pipes fill at the rate of 1/15 + 1/24 pool per hour
So:
1/15 + 1/24 = 1/x multiply each term by 120x
8x+5x=120
13x=120
x=120/13 hours (almost 9 1/4 hours)
CK
in 120/13 hours Pipe A fills(1/15)(120/13)=8/13 of the pool
in 120/13 hours Pipe B fills (1/24)(120/13)=5/13 of the pool
5/13 +8/13=13/13=1 pool filled
Hope this helps---ptaylor
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