SOLUTION: I am having a very hard time with understanding how to come up with an answer to this word problem. During the first part of a trip, a canoeist travels 91 miles at a certain speed

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Question 522953: I am having a very hard time with understanding how to come up with an answer to this word problem. During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?
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1st part DATA:
distance = 91 miles ; rate = r mph ; time = d/r = 91/r hrs
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2nd part DATA:
distance = 21 miles ; rate = r-5 mph ; time = d/r = 21/(r-5) hrs
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Equation:
time + time = 5 hrs
91/r + 21/(r-5) = 5
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91(r-5) + 21r = 5r(r-5)
112r - 455 = 5r^2-25r
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Rearrange:
5r^2 - 137r + 455 = 0
Positive solution:
r = 23.5331 mph (1st part speed)
r-5 = 18.5331 mph (2nd part speed)
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Cheers,
stan H.
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Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
t = d / r

(91 / s) + [21 / (s - 5)] = 5

multiplying by s(s-5) the LCD ___ 91s - 455 + 21s = 5s^2 - 25s

0 = 5s^2 - 137s + 455

use quadratic formula to find s ___ there will be 2 solutions, but only one will check