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Question 662692: working together, Dan and Leah can mow a lawn in 1hour and 12 min. working alone , Leah can mow the lawn in 1hour less time than it would take Dan. Find the time it takes for each of them working alone?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! working together, Dan and Leah can mow a lawn in 1hour and 12 min. working alone , Leah can mow the lawn in 1hour less time than it would take Dan. Find the time it takes for each of them working alone?
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Note: 1 hr 12 min = 6/5 hours
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Dan DATA: time = x hrs/job ; rate = 1/x job/hr
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Leah DATA: time = x-1 hrs/job ; rate = 1/(x-1) job/hr
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Together DATA: time = 6/5 hrs/job ; rate = 5/6 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x-1) = 5/6
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6(x-1) + 6x = 5x(x-1)
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6x-6 + 6x = 5x^2 - 5x
5x^2 -17x +6 = 0
x = 3 hrs (Dan's time to do the job alone)
x-1 = 2 hrs (Leah's time to do the job alone)
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Cheers,
Stan H.
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