Find the cyclist's rate during the first portion and his rate during the cool-down portion.

Question

An amateur cyclist is training for a road race. He rode the first 48-mile portion of his workout at a constant rate. He then reduced his speed by 3 mph for the remaining 39-mile cool-down portion of the workout. Each portion of the workout took equal time. Find the cyclist's rate during the first portion and his rate during the cool-down portion.

Answer 1

48 = R*t

39 = (R-3)*t

48/r = 39/(R-3)

48(r-3) = 39r

48r - 144 = 39r

9r - 144 = 0

9r = 144

r = 16

16 mph for 48 miles takes 3 hours

13 mph for 39 miles takes 3 hours