SOLUTION: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18 h using both hoses. They also know that Bob's hose, used alone, t
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Question 1152113: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 70% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = time to fill pool with Jim's alone
= time to fill pool with Bob
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Add their rates of filling to get rate filling together
Multiply both sides by
and
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Bob's hose alone takes 23.4 hrs
Jim's hose alone takes 78 hrs
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check:
close enough
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
The solution from the other tutor is a perfectly good formal algebraic solution.
If a formal algebraic solution is not required, here is an alternative method for solving the problem.
To fill the whole pool alone, Bob's hose take 70% less time than Jim's. So if the time required by Jim's hose is x, the time required by Bob's hose is x minus 70% of x, which is 0.3x.
So the ratio of the times required by the two hoses is 1:0.3, or 10:3.
In working together, then, the fraction of the job that Bob's hose does is 10/13, and the fraction Jim's hose does is 3/13.
We know that working together the two hoses take 18 hours to fill the pool.
So in 18 hours, Bob's hose fills 10/13 of the pool, and Jim's hose fills 3/13 of the pool.
That means the number of hours required for Bob's hose to fill the whole pool by itself is ; and the number of hours required for Jim's hose to fill the pool by itself is .
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