SOLUTION: It takes one pipe 4 hours more to empty a pool than it takes another pipe to fill the pool. If both pipes are accidentally left open, it takes 24 hours to fill the pool. How long

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes one pipe 4 hours more to empty a pool than it takes another pipe to fill the pool. If both pipes are accidentally left open, it takes 24 hours to fill the pool. How long      Log On


   

Question 968996: It takes one pipe 4 hours more to empty a pool than it takes another pipe to fill the pool. If both pipes are accidentally left open, it takes 24 hours to fill the pool. How long does it take a single pipe to fill the pool?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
It takes one pipe 4 hours more to empty a pool than it takes another pipe to fill the pool. If both pipes are accidentally left open, it takes 24 hours to fill the pool. How long does it take a single pipe to fill the pool?
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let x=time it takes fill pipe to fill the pool by itself
1/x=its fill rate
x+4=time it takes drain pipe to empty the pool by itself
1/(x+4)=its drain rate
24=time it takes to fill the pool with both pipes open
1/24=their fill rate
1%2Fx-1%2F%28x%2B4%29=1%2F24
lcd:24x(x+4)
24(x+4)-24x=x(x+4)
24x+96-24x=x^2+4x
x^2+4x-96=0
(x-8)(x+12)=0
x=8
How long does it take a single pipe to fill the pool? 8 hrs