SOLUTION: a cyclist traveled 60 mi at a constant rate before reducing the speed by 7mph. Another 40 mi was traveled at the reduced speed. The total time for the 100-mile trip was 9 h. Find t

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a cyclist traveled 60 mi at a constant rate before reducing the speed by 7mph. Another 40 mi was traveled at the reduced speed. The total time for the 100-mile trip was 9 h. Find t      Log On

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Question 860964: a cyclist traveled 60 mi at a constant rate before reducing the speed by 7mph. Another 40 mi was traveled at the reduced speed. The total time for the 100-mile trip was 9 h. Find the rate during the first 60 mi.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a cyclist traveled 60 mi at a constant rate before reducing the speed by 7mph. Another 40 mi was traveled at the reduced speed. The total time for the 100-mile trip was 9 h. Find the rate during the first 60 mi.
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Original leg DATA:
dist = 60 miles ; rate = x mph; time = 60/x hrs
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2nd leg DATA:
distance = 40 miles ; rate = x-7 mph ; time = 40/(x-7) hrs
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Equation:
time + time = 9 hrs
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60/x + 40/(x-7) = 9
60(x-7) + 40x = 9x(x-7)
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100x - 420 = 9x^2 - 63x
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9x^2 - 163x + 420 = 0
x = 15 mph
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Cheers,
Stan H.
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