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?

Question

Mohamed

Mathematics

18 February, 16:27

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?

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Helena Trevino · Answer 1

Answer: 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