Answer: Leanna ran 40.08 miles before she was passed by Irina.
Step-by-step explanation:
Let t represent the number of hours that Leanna ran before she was passed by Irina.
Leanna started in group E and ran at a rate of 4.8 miles per hour.
Distance = speed × time
Distance that Leanna ran in t hours is
4.8 × t = 4.8t
During the race, she was passed by Irina who ran at a rate of 5 miles per hour and started in group H, 20 minutes after Leanna started. 20 minutes = 20/60 = 1/3 hours. This mean that the number of hours that Irina ran before she passed Leanna is (t - 1/3) hours.
Distance that Irina ran would be
5(t - 1/3) = 5t - 5/3
Since they covered the same distance, then
4.8t = 5t - 5/3
5t - 4.8t = 5/3
0.2t = 1.67
t = 1.67/0.2 = 8.35 hours
Distance that Leanna ran before she was passed by Irina is
4.8t = 4.8 × 8.35 = 40.08 miles
