SOLUTION: During the first part of a trip, a canoeist travels 35 miles at a certain speed. The canoeist travels 14 miles on the second part or the trip at a speed 5 mph slower. The total tim

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: During the first part of a trip, a canoeist travels 35 miles at a certain speed. The canoeist travels 14 miles on the second part or the trip at a speed 5 mph slower. The total tim      Log On


   

Question 619280: During the first part of a trip, a canoeist travels 35 miles at a certain speed. The canoeist travels 14 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What is the speed on each part of the trip?
(not understanding how to put this together!)
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
(35 / s) + [14 / (s - 5)] = 2

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 35 miles at a certain speed. The canoeist travels 14 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What is the speed on each part of the trip?
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1st leg DATA:
distance = 35 miles ; rate = x mph ; time = d/r = 25/x hrs
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2nd leg DATA:
distance = 14 miles ; rate = x-5 mph ; time = d/r = 14/(x-5) hrs
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Equation:
time + time = 2 hrs
25/x + 14/(x-5) = 2 hrs
25(x-5) + 14x = 2x(x-5)
25x - 125 + 14x = 2x^2 - 10x
2x^2 -49x + 125 = 0
x = 21.607 mph (rate on 1st leg)
x-5 = 16.607 mph (rate on 2nd leg)
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cheers,
Stan H.
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