SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 101 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 101 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How       Log On


   

Question 901184: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 101 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?
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/(x-15)+1/x=1/101
x = 209.78
x=210 x-15=195
1/(x+15)+1/x=1/101
x = 195 x+15=210
Much too complicated for this type problem

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 101 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?
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Together rate:: 1/101 job/min
Bobby rate:: 1/x job/min
Billy rate:: 1/(x-15) job/min
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Eqution:
rate + rate = together rate
1/x + 1/(x-15) = 1/101
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101(x-15) + 101x = x(x-15)
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101x - 101*15 + 101x = x^2 -15x
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x^2 - 15x - 202x + 101*15 = 0
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x^2 -217x + 101*15 = 0
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Ans: x = 209.77 min (Bobby's time alone)
x-15 = 194.77 min (Billy's time alone)
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Cheers,
Stan H.
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