HELP! I HAVE BEEN STUCK FOR HOURS! 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 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

the answer on e2020 was d.