Answer:
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.
