MAT117
posted by Leina'ala .
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?

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. 
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