SOLUTION: A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he

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Question 277650: A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?
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Let his walking rate be w mph
Then his biking rate is w+5.4 mph
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Bike DATA:
distance = 32.4 mi; rate = (w+5.4) mph ; time = d/r = 32.4/(w+5.4)hrs.
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Walk DATA:
distance = 32.4 mi ; rate = w mph ; time = d/r = 32.4/w hrs.
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Equation:
time + time = 12.6 hrs
32.4/(w+5.4) + 32.4/w = 12.6
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Multiply thru by 10:
324/(w+5.4) + 324/w = 126
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Multiply thru by w(w+5.4) to get:
324w + 324(w+5.4) = 126w(w+5.4)
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648w + 1749.6 = 126w^2 + 680.4w
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126w^2 + 32.4w - 1749 = 0
w = -3.599 or w = 3.857
Positive solution:
walking rate = 3.857 mph
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Cheers,
Stan H.