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

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) (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.
---------------------------------------------
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
==================================
Cheers,
Stan H.
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