Question 948114: To travel 110 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 72 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! To travel 110 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 72 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.
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Doreen DATA:
dist = 72 miles ; time = x hrs ; rate = d/t = 72/x mph
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Sue DATA:
dist = 110 miles ; time = x-3 hrs ; rate = d/t = 110/(x-3) mph
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Equation::
Sue = Doreen + 13
110/(x-3) = [72/x] + 13
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110x = 72(x-3) + 13x(x-3)
110x = 72x - 216 + 13x^2 - 39x
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38x = -216 + 13x^2 - 39x
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13x^2 -77x -216 = 0
Positive solution::
x = 8
Doreen rate = 72/8 = 9 mph
Sue rate = 110/(8-3) = 22 mph
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Cheers,
Stan H.
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