Question

m.14 solve equations with variables on both sides: word probl...
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?
20s + 6 = 8s
20 + 6s = 8s
how long will it take for billy to catch up to reggie?
simplify any fractions.
□ seconds

Explanation:

Part 1: Choosing the Correct Equation

Step1: Analyze Reggie's distance

Reggie starts 20 meters ahead and runs at 6 m/s for \( s \) seconds. So his total distance is \( 20 + 6s \).

Step2: Analyze Billy's distance

Billy runs at 8 m/s for \( s \) seconds, so his distance is \( 8s \).

Step3: Set distances equal (catch - up)

When Billy catches up, their distances are equal. So the equation is \( 20 + 6s = 8s \).

Step1: Subtract \( 6s \) from both sides

\( 20+6s - 6s=8s - 6s \)
Simplifies to \( 20 = 2s \).

Step2: Divide both sides by 2

\( \frac{20}{2}=\frac{2s}{2} \)
Simplifies to \( s = 10 \).

Answer:

\( 20 + 6s = 8s \)

Part 2: Solving for \( s \)