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.

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