Question 449392: Nancy and Liz are working on a take-home test. Normally, Liz finishes a take-home test in 2 hors less time than Nancy. Nancy works by herself for 3 hours, then when Liz comes along, together, they finish the job in 2 more hours. How many hours does it take Nancy to the test on her own?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Nancy and Liz are working on a take-home test.
Normally, Liz finishes a take-home test in 2 hours less time than Nancy.
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Let Nancy's time be x hrs/job ; Nancy rate = 1/x job/hr.
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Then Liz's time is x-2 hrs/job ; Liz rate = 1/(x-2) job/hr
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Nancy works by herself for 3 hours, then when Liz comes along, together, they finish the job in 2 more hours.
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3(1/x) + 2(1/x + 1/x-2) = 1 job
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How many hours does it take Nancy to the test on her own?
Solve for "x":
(3/x) + (2/x) + 2/(x-2) = 1
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Multiply thru by x(x-2) to get:
3(x-2) + 2(x-2) + 2x = x(x-2)
7x -10 = x^2-2x
x^2-9x+10 = 0
(x-10)(x+1) = 0
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Positive solution:
x = 10 hrs (Nancy's time to do the job alone)
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Cheers,
Stan H.
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