Mrs. Montoya, the P. E. Teacher, is pairing off students to race against each other. Lara can run 5 5 meters per second, and Riley can run 7 7 meters per second. Mrs. Montoya decides to give Lara a head start of 12 12 meters since she runs more slowly. Once the students start running, Riley should catch up to Lara. How far will Riley have to run to catch up to Lara? How long will that take?

Riley will catch up with Lara after 6 seconds

Step-by-step explanation:

Let t represent the time it will take Riley to catch up with Lara. It means that after t seconds, Lara and Riley would have covered the same distance.

Distance = speed × time

Lara can run 5 meters per second. It means that the distance covered by Lara in t seconds is 5t meters

Mrs. Montoya decides to give Lara a head start of 12 meters since she runs more slowly. it means the total distance covered by Lara after t seconds is

5t + 12

Riley can run 7 meters per second. It means that the distance covered by Riley in t seconds is 7t meters.

Since the distance covered after t seconds is the same, then

7t = 5t + 12

7t - 5t = 12

2t = 12

t = 12/2

t = 6 seconds