Answer
Michelle rode for 2.5 hours.
Karen rode for 3 hours.
Work Step by Step
Let t represent the time Michelle rode. Karen rode 30 minutes more, so she rode t + 0.5 hours.
Karen rode at 15 miles per hour, so she rode for a distance of (t + 0.5) $\times$ 15 = 15t + 7.5 miles.
Michelle rode at 14 miles per hour, so she rode for a distance of t $\times$ 14 = 14t miles.
Karen rode 10 miles farther than Michelle, which means the distance she rode was 10 more than the distance Michelle rode.
So, we can set up the following equation:
15t + 7.5 = 14t + 10
t = 10 - 7.5
t = 2.5
Michelle rode for 2.5 hours.
Karen rode for t + 0.5 = 2.5 + 0.5 = 3 hours.
