During the first part of a trip, a canoeist travels 32 miles at a certain speed. The canoeist travels 8 miles on the second part of the trip at a speed 5 mph slower. The total time for this trip is 2 hours. What was the speed on each part of the trip?

Time for 1st part of trip + time for 2nd part of trip = 2 hours

Let x = speed for 1st part of trip

(x - 5) = speed for 2nd part of trip

Distance = speed * time

1st part of trip

32 = x * time #1

Time #1 = 32/x

2nd part of trip

8 = (x - 5) * time #2

Time #2 = 8/(x - 5)

Time #1 + Time #2 = 2

32/x + 8/(x - 5) = 2

both sides by x * (x - 5)

32 * (x - 5) + 8x = 2 * x * (x - 5)

32x - 160 + 8x = 2x^2 - 10x

40x - 160 = 2x^2 - 10x

50x - 160 = 2x^2

2x^2 - 50x + 160 = 0

Divide by 2

x^2 - 25x + 80 = 0