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.

Question

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?

20s+6=8s

20+6s=8s

Answer 1

To find the time \( s \) it will take for Billy to catch up to Reggie, we can set up an equation based on their distances.

Reggie's starting distance is 20 meters ahead, and he runs at 6 meters per second. The distance he covers after \( s \) seconds is:

\[ \text{Distance}_{Reggie} = 20 + 6s \]

Billy starts from 0 meters but runs faster at 8 meters per second. The distance he covers after \( s \) seconds is:

\[ \text{Distance}_{Billy} = 8s \]

To find when Billy catches up to Reggie, we set the distances equal to each other:

\[ 8s = 20 + 6s \]

Now, we can rearrange this equation to solve for \( s \):

\[ 8s - 6s = 20 \]

This simplifies to:

\[ 2s = 20 \]

Dividing both sides by 2 gives:

\[ s = 10 \]

Thus, the correct equation to use to find \( s \) is:

\[ 8s = 20 + 6s \]

From the options you provided, the equation \( 20 + 6s = 8s \) would be the appropriate choice.