Answer: the cyclist's speed during the first portion is 10 mph and his speed during the cool down portion is 8 mph.
Step-by-step explanation:
Let x represent the cyclist's rate during the first portion.
The amateur cyclist training for a road race rode the first 20 mile
portion of his workout at a constant rate.
Time = distance/speed
Time taken to ride through the first portion is
20/x
For the next 16 mile cool down portion of his workout, he reduced his speed by 2 miles per hour. It meas that his speed during the cool down portion is (x - 2) mph. Time taken to ride through the cool down portion is
16/(x - 2)
Since each portion of the workout took the same time, it means that
20/x = 16/(x - 2)
Cross multiplying, it becomes
20(x - 2) = 16x
20x - 40 = 16x
20x - 16x = 40
4x = 40
x = 40/4
x = 10 mph
His speed during the cool down portion is
10 - 2 = 8 mph
