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?
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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