Question

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

If the answer is not an integer, enter it as an exact decimal.

Answer 1

Answer: 21.3 miles

Explanation:

At the point where Sophia was passed by Josefina, they would have covered the same distance.

Let t represent the time spent by Sophia before she was passed by Josefina.

Distance = speed × time

Sophia started in group E and ran at a rate of 4.8 miles per hour. The distance covered by Sophia before she was passed by Josefina is

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 = 0.417 hour) after Sophia started. The time spent by Josefina in covering this distance is t - 0.417

Distance covered by Josefina is

5.3(t - 0.417) = 5.3t - 2.21

Since the distance covered is the same, then

4.8t = 5.3t - 2.21

5.3t - 4.8t = 2.21

0.5t = 2.21

t = 2.12/0.5 = 4.42 hours

Therefore, the distance that Sophia ran before she was passed by Josefina is

4.8 × 4.42 = 21.3 miles