Please help me with this question!

12 miles

Step-by-step explanation:

Let the amount of hours it takes Leroy to catch up to Kevin equal x. Since speed multiplied by time is distance, Leroy would have run a total of 6x miles(6*x). Kevin already had a head start of 24 minutes, which is the same as 2/5 of an hour. In 2/5 an hour, Kevin ran 2 miles as 2 is 2/5 *5. For the next x hours his distance would be a total of 5x(5*x). This means, after x hours, Kevins distance is 5x + 2. In this case, catching up to someone is the same as having the same distance value. This means we can set the two expressions equal to each other, and solve:

6x = 5x + 2

x = 2

The time it took Leroy to catch up is 2 hours, but we are looking for the distance, which is represented by 6x. We substitute in 2 to get:

6(2) = 12

This means Leroy had to run 12 miles.

See below.

Step-by-step explanation:

Triangle ABC is congruent to triangle DEF (Given)

Angle ACB is congruent to angle ECG. (Vertical angles theorem)

Angle CEG is congruent to angle DEF. (Vertical angles theorem)

Angle DEF is congruent to angle ABC. (Definition of congruent triangles)

Angle CEG is congruent to angle ABC. (Substitution property of equality).

Triangle ABC is similar to triangle GEC. (Angle angle similarity postulate- if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.)