SOLUTION: During the first part of a trip, a canoeist travels 44 miles at a certain speed. The canoeist travels 15 miles on the second part of the trip at a speed 5 mph slower. The total tim

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Question 581351: During the first part of a trip, a canoeist travels 44 miles at a certain speed. The canoeist travels 15 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
During the first part of a trip, a canoeist travels 44 miles at a certain speed. The canoeist travels 15 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?
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1st Part DATA:
distance = 44 miles ; rate = x mph ; time = d/r = 44/x hrs
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2nd part DATA:
distance = 15 miles ; rate = (x-5)mph ; time = d/r = 15/(x-5)
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Equation:
time + time = 5 hrs
44/x + 15/(x-5) = 5
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Multiply thru by x(x-5) to get:
44(x-5) + 15x = 5x(x-5)
44x - 220 + 15x = 5x^2-25x
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59x-220 = 5x^2-25x
5x^2 - 69x + 220 = 0
Usable solution:
x = 8.8 mph (1st part rate)
x-5 = 3.8 mph (2nd part rate)
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Cheers,
Stan H.