MAT117

During the first part of a trip, a canoeist travels 68 miles at a certain speed. The canoeist travels 16 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?

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  1. 68mi @ (X+5)mi/h.
    16mi @ xmi/h.

    t = 68 / (X+5) + 16 / X = 3h,
    LCM = X(X+5):
    (68X + 16(X+5)) / X(X+5) = 3,
    (84X + 80) / X(X+5) = 3,
    Multiply both sides by X(X+5):
    84X + 80 = 3X(x+5),
    84X + 80 = 3X^2 + 15X,
    3X^2 + 15X - 84X - 80 = 0,
    3X^2 - 69X - 80 = 0.
    Solve for X using the Quad. Formula and
    get:
    X = 24.1062, and - 1.1062.
    Select the + value of X:
    X = 24.1062mi/h.
    X+5 = 29.1062mi/h.

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  2. during the first part of the trip a canoeist travels 24 miles at a certain speed. the canoeist travels 7 miles on the second part of the trip at speed of 5 mpg slower. the total time for the trip is 3 hrs. what is the speed of each trip

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