SOLUTION: working together, dan and julio can mow a lawn in 12 minutes. Julio can mow the lawn by himself in 10 minutes less than it takes Dan by himself. How long does it take each of the

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Question 353458: working together, dan and julio can mow a lawn in 12 minutes. Julio can mow the lawn by himself in 10 minutes less than it takes Dan by himself. How long does it take each of them to mow the lawn alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
working together, dan and julio can mow a lawn in 12 minutes. Julio can mow the lawn by himself in 10 minutes less than it takes Dan by himself. How long does it take each of them to mow the lawn alone?
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together rate = 1/12 job/min
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Let Dan time = x min/job; rate = 1/x job/min
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Julio time = x-10 min/job ; rate = 1/(x-10) job/min
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Equation:
rate + rate = together rate
1/x + 1/(x-10 = 1/12
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12(x-10) + 12x = x(x-10)
24x-120 = x^2-10x
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x^2 - 34x + 120 = 0
(x-30)(x-4) = 0
Realistic time for Dan so Julio's time will not be negative:
x = 30 Min (time required for Dan to do the job alone)
x-10 = 20 min (time required for Julio to do the job alone)
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cheers,
Stan H.