SOLUTION: To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen to travel 56 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find

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Question 792404: To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen to travel 56 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen to travel 56 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 = 88 miles; x-4 hrs ; rate = 88/(x-4) hours
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Doreen DATA:
distance = 56 miles; x hrs ; rate = 56/x hours
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Equation:
88/(x-4) - 56/x = 15 mph
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88x - 56(x-4) = 15x(x-4)
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88x - 56x + 56*4 = 15x^2 - 60x
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32x + 224 = 15x^2-60x
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15x^2 - 92x - 224 = 0
x = 8 hours
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Etc.
Cheers,
Stan .

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Doreen rate --------x mph----------------------56 miles
sue rate ------------x+15 mph------------------88 miles
t=d/r
Sue time - Doreen time = 4 hours

56/x - 88/(x+15) =4
multiply by x(x+15)
56(x+15)-88x=4x(x+15)
56x+840-88x=4x^2+60x
-32x+840=4x^2+60x
4x^2+60x+32x-840=0
4x^2+92x-840=0
/4
x^2+23x-210=0
x^2+30x-7x-210=0
x(x+30)-7(x+30)=0
(x+30)(x-7)=0
x=-30 OR x=7
ignore negative
x= 7 speed of Doreen
7+15 = 22 mph speed of Sue