In a large marathon, runners start the race in stages. Leanna started in group E and ran at a rate of 4.8 miles per hour. 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. How far did Leanna run before she was passed by Irina?

Leanna ran 39.96 miles before she was passed by Irina.

Step-by-step explanation:

When Irina would pass Leanna, they would have ran the same distance.

Let t represent the time that Leanna ran before she was passed by Irina.

Distance = speed × time

Leanna started in group E and ran at a rate of 4.8 miles per hour. The distance ran by Leanna before she was passed by Irina 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(20/60 = 0.333 hour) after Leanna started. The time spent by Irina in running this distance is

t - 0.333

Distance ran by Irina is

5(t - 0.333) = 5t - 1.665

Since they ran the same distance, then

4.8t = 5t - 1.665

5t - 4.8t = 1.665

0.2t = 1.665

t = 1.665/0.2 = 8.325 hours

Therefore, the distance that Leanna ran before she was passed by Irina is

4.8 × 8.325 = 39.96 miles