Question 78016: Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
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Winston DATA:
Time = x-1 hrs/job ; Rate = 1/(x+1) job/hr
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Willie DATA:
time = x hrs/job ; Rate = 1/x job/hr
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Together DATA:
Time = 2 hrs/job ; Rate = 1/2 job hr
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EQUATION:
rate + rate = together rate
1/(x+1) + 1/x = 1/2
(x+x+1)/(x(x+1)) = 1/2
Multiply both sides by x(x+1)
2(2x+1) = x(x+1)
4x+2 = x^2+x
x^2-3x-2=0
x=[3+-sqrt(9-4*-2)]/2
x=[3+-sqrt(17)]/2
x=[3.56 hrs is the only positive answer.
x+1=4.56 hrs (time Winston needs to do the job alone)
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Cheers,
Stan H.
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