SOLUTION: During the first part of a trip, a canoeist travels 54 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower. The total

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Question 142315This question is from textbook Intermediate Algebra
: During the first part of a trip, a canoeist travels 54 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower. The total time of the trip is 3 hours. What was the speed on each part of the trip? This question is from textbook Intermediate Algebra

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 54 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower. The total time of the trip is 3 hours. What was the speed on each part of the trip?
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1st Part DATA:
distance = 54 ; rate = x mph ; time = 54/x hrs
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2nd Part DATA:
distance = 22 ; (x-5) mph ; time = 22/(x-5) hrs
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EQUATION:
time + time = 3 hrs
(54/x) + (22/(x-5)) = 3
54x-270 + 22x = 3x(x-5)
76x -270 = 3x^2-15x
3x^2 - 91x + 270 = 0
x = 27 mph(speed on 1st part)
x-5 = 22 (speed on 2nd part)
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Cheers,
Stan H.