A cyclist rode the first 26 -mile portion of his workout at a constant speed. For the 18 -mile cooldown portion of his workout, he reduced his speed by 4 miles per hour. Each portion of the workout took the same time. Find the cyclist's speed during the first portion and find his speed during the cooldown portion.

Answer: the cyclist's speed during the first portion is 13 mph and his speed during the cool down portion is 9 mph.

Step-by-step explanation:

Let x represent the cyclist's speed during the first portion.

The cyclist rode the first 26 -mile portion of his workout at a constant speed.

Time = distance/speed

Time taken to ride through the first portion is

26/x

For the 18 -mile cool down portion of his workout, he reduced his speed by 4 miles per hour. It meas that his speed during the cool down portion is (x - 4) mph. Time taken to ride through the cool down portion is

18 / (x - 4)

Since each portion of the workout took the same time, it means that

26/x = 18 / (x - 4)

Cross multiplying, it becomes

26 (x - 4) = 18x

26x - 104 = 18x

26x - 18x = 104

8x = 104

x = 104/8

x = 13 mph

His speed during the cool down portion is

13 - 4 = 9 mph