SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How l

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Question 468204: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time than it would take Bobby. How long would it take Bobby to mow the lawn by himself?
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Together time = 69 min/job ; rate = 1/69 job/min
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Billy time = x-15 min/job ; rate = 1/(x-15) job/min
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Bobby time = x min/job ; rate = 1/x job/min
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Equation:
rate + rate = together rate
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1/x + 1/(x-15) = 1/69
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69(x-15) + 69x = x(x-15)
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138x-69*15 = x^2-15x
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x^2 -15x -138x + 69*15 = 0
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x^2 - 153x + 69*15 = 0
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x = [153 +- sqrt(153^2 - 4*69*15)/2
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x = [153 +- sqrt(19269)]/2
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Realistic answer:
x = 145.91 minutes (Bobby's time)
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x-15 = 130.91 minutes (Billy's time)
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Cheers,
Stan H.
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