SOLUTION: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 24 h using both hoses. They also know that Bob's hose, used alone, t

Question 756485: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 24 h using both hoses. They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
and help with this one too..
thanks:)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 24 h using both hoses. They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
.
Let x = time (hours) it takes for Jim's hose alone
then
.5x = time(hours) it takes for Bob's hose alone
.
24(1/x + 1/(.5x)) = 1
multiply both sides by .5x:
24(1/x + 1/(.5x)) = .5x
24(.5 + 1) = .5x
24(1.5) = .5x
36 = .5x
36/.5 = x
72 hours = x (Jim's hose)
.
Bob's hose:
.5x = .5(72) = 36 hours

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