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.