Question

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? ​

Answer 1

Answer: Riley will catch up with Lara after 6 seconds

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