Caitlin recently rode her bicycle to visit her friend who lives 9 miles away. On her way there, her average speed was 8 miles per hour faster than on her way home. If Caitlin
spent a total of 3 hours bicycling, find the two rates.

15 points help me please. show steps!!

12 mph & 4 mph

Step-by-step explanation:

Let s and s - 8 be the speed of Caitlin going on her friend and her speed on her way home respectively.

Distance = Speed × Time

Distance/Speed = Time

9/s + 9/(s - 8) = 3

9(s - 8) + 9s = 3s(s - 8)

9s - 72 + 9s = 3s² - 24s

3s² - 42s + 72 = 0

s² - 14s + 24 = 0

(s - 2)(s - 12) = 0

s - 2 = 0

s = 2

s - 12 = 0

s = 12

If s = 2, then s - 8 = - 6 < 0. We want s and s - 8 to be positive so s = 12 mph. It follows that her speed on her way home is 4 mph.