Question 761492: To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 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 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.
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Sue DATA:
distance = 154 miles ; time = x-3 hrs ; rate = d/t = 154/(x-3) mph
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Doreen DATA:
distance = 70 miles ; time = x hrs ; rate = 70/x mph
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Equation:
rate - rate = 15 mph
154/(x-3) - 70/x = 15
154x - 70(x-3)=15x(x-3)
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154x - 70x + 210 = 15x^2 - 15x
84x + 210 = 15x^2 - 15x
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15x^2 - 99x - 210 = 0
5x^2 - 33x - 70 = 0
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Positive solution:
x = 8.89 hrs (Doreen time) ; 70/8.289 = 8.445 mph (Doreen rate)
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x-3 = 5.89 hrs (Sue time) ; 154/5.89 = 18.24 mph (Sue rate)
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Cheers,
Stan H.
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