A Cyclist rode the first 30-mile portion of his workout at a a constant speed. For the 24-mile cooldown portion of his workout, he reduced his speed by 3 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

let s = his speed on the 1st 30 mi

then

(s-2) = his speed on the last 24 mi

:

Write time equation, time = dist/speed

:

workout time = cooldown time

30/s = 24/s-2

Cross multiply

30(s-2) = 24s

30s - 60 = 24s

30s - 24s = 60

6s = 60

s = 10 mph his workout speed

then

10 mph his cooldown speed

:

:

Check this by finding the actual times, they should be equal

30/10 = 3 hrs

24/10 = 2.4 hrs

Since the actual time is not equal there must be some mistake in the question