Question 899068: Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)
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Jenny DATA:
distance = 60 miles ; time = x-2 hrs ; rate = d/t = 60/(x-2) mph
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Maureen DATA:
distance = 50 miles ; time = x hrs ; rate = 50/x mph
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Equation:
rate - rate = 10 mph
60/(x-2) - 50/x = 10 mph
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60x - 50(x-2) = 10x(x-2)
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10x + 100 = 10x^2 -20x
10x^2 -30x - 100 = 0
x^2 - 3x - 10 = 0
(x-5)(x+2) = 0
Positive solution::
x = 5
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Maureen DATA: time = x = 5 hrs ; rate = 50/5 = 10 mph
Jenny DATA: time = x-2 = 3 hrs ; rate = 60/3 = 20 mph
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Cheers,
Stan H.
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