Answer: Sophia ran 21.2 miles before she was passed by Josefina.
Explanation:
Let t represent the time for which Sophia ran before she was passed by Josefina.
Sophia started in group E and ran at a rate of 4.8 miles per hour.
Distance = speed × time
Distance covered by Sophia in t hours would be
4.8 × t = 4.8t
During the race, she was passed by Josefina who ran at a rate of 5.3 miles per hour and started in group H, 25 minutes(25/60 = 5/12 hours) after Sophia started. This mean that time spent by Josefina before she passed Sofia is (t - 5/12) hours.
Distance covered by Josefina would be
5.3(t - 5/12) = 5.3t - 26.5/12
Since they covered the same distance, then
4.8t = 5.3t - 26.5/12
5.3t - 4.8t = 26.5/12
0.5t = 26.5/12
t = 2.208/0.5 = 4.417 hours
Distance run by Sophia before she was passed by Josefina is
4.8t = 4.8 × 4.417 = 21.2 miles