SOLUTION: During the first part of a trip a conoeist travels 54 miles at a certain speed. The conoeist travels 8 miles on the second part of the trip at a speed 5mph slower. Total time of t

Question 320599: During the first part of a trip a conoeist travels 54 miles at a certain speed. The conoeist travels 8 miles on the second part of the trip at a speed 5mph slower. Total time of the trip is 3hrs. What was the speed of each part of the trip?
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!

Let x be the speed for the first part of the trip. So that part takes 54/x hours.
So the speed for the second part of the trip is x - 5, so that part takes 8/(x-5).
Therefore:
(54/x) + (8/(x-5)) = 3
54(x - 5) + 8x = 3x(x - 5)
54x - 270 + 8x = 3x^2 - 15x
62x - 270 = 3x^2 - 15x
3x^2 - 15x - 62x + 270 = 0
3x^2 - 77x + 270 = 0
x = (-(-77) +/- sqrt((-77)^2 - 4(3)(270))) / (2*3)
x = (77 +/- sqrt(5929 - 3240)) / 6
x = (77 +/- sqrt(2689)) / 6
x =~ 21.4759 or 4.19
If x =~ 4.19, then the speed for the first part of the trip is 4.19, and the speed for the second part of the trip is -0.81. But a negative number makes sense, so we'll discount that solution.
Therefore, x =~ 21.4759, so the speed for the first part of the trip is about 21.4759, so the speed for the second part of the trip is about 16.4759.

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