Question

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Billy and his younger brother, Reggie, are going to race each other to the park. They will start running at the same time, but Billy is letting Reggie start 20 meters ahead. Billy can run 8 meters per second, and Reggie can run 6 meters per second.
Which equation can you use to find s, the number of seconds it will take for Billy to catch up to Reggie if they each run as fast as they can?
How long will it take for Billy to catch up to Reggie?
Simplify any fractions.

Answer 1

Let s be the number of seconds after they start. Reggie's distance = 20 + 6s, Billy's distance = 8s. Set them equal:

8s = 6s + 20

Solve: 8s − 6s = 20 → 2s = 20 → s = 10 seconds.

So it takes Billy 10 seconds to catch Reggie.