The cyclist's speed during the first portion was ? miles per hour and his speed during the second portion was ? miles per hour

Question

A cyclist rode the first 24-mile portion of his workout at a constant speed. For the 15-mile cooldown portion, 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.

Answer 1

distance=rate*time

d=rt

24=rt

15=(r-3)t

 

24/r=t

15/(r-3)=t

equate the two because they are both equal to t

24/r=15/(r-3)

cross multiply

15*r=24*(r-3)

15r=24r-72

72=24r-15r

72=9r

r=8 mph for the first portion

r-3=5 mph for the second portion