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Question 894749: It takes Jack 15 hours longer to drain a basement than Jill. If they work together, it takes 4 hours to drain a basement. How long does it take for each person to working alone?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! It takes Jack 15 hours longer to drain a basement than Jill. If they work together, it takes 4 hours to drain a basement. How long does it take for each person to working alone?
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Draining the basement is the job.
Jill does it in some number, J, of hours, so she does 1/J per hour.
Jack does it in J+15 hours, so he does 1/(J+15) per hour.
Together, they do 1/J + 1/(J+15) per hour, and it takes them 4 hours.
Together, the do 1/4 of the job.
---> 1/J + 1/(J+15) = 1/4
Can you solve for J ?
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! It takes Jack 15 hours longer to drain a basement than Jill. If they work together, it takes 4 hours to drain a basement. How long does it take for each person to working alone?
Jack DATA:
time = x + 15 hrs/job ; rate = 1/(x+15) job/hr
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Jill DATA:
time = x hrs/job ; rate = 1/x job/hr
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Together DATA:
time = 4 hrs/job ; rate = 1/4 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+15) = 1/4
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Multiply thru by 4x(x+15) to get::
4(x+15) + 4x = x(x+15)
4x + 60 + 4x = x^2 + 15x
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x^2 + 7x - 60 = 0
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(x+12)(x-5) = 0
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Positive solution:
x = 5 hrs (Jill's time)
x+15 = 20 hrs (Jack's time)
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Cheers,
Stan H.
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