Question 940120: 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.)
How fast is Jenny and Maureen going in mph?
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.)
How fast is Jenny and Maureen going in mph?
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Jenny DATA:
dist = 60 miles ; time = x-2 hrs ; rate = d/t = 60/(x-2) mph
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Maureen DATA:
dist = 50 miles ; time = x hrs ; rate = d/t = 50/x mph
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Equation:
Jenny rate - Maureen rate = 10 mph
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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
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x + 10 = x^2 - 2x
x^2 - 3x - 10 = 0
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(x-5)(x+2) = 0
Positive solution:
x = 5 hrs
Jenny rate = 60/3 = 20 mph
Maureen rate = 50/5 = 10 mph
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Cheers,
Stan H.
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