Question

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:

First Sub - Question (Equation Selection)

To find the equation, we use the formula \( \text{distance}=\text{speed}\times\text{time} \). Reggie starts 20 meters ahead and runs at 6 meters per second, so his total distance is \( 20 + 6s \). Billy runs at 8 meters per second, so his distance is \( 8s \). When Billy catches up, their distances are equal, so the equation is \( 20+6s = 8s \). The first equation \( 20s + 6=8s \) is incorrect as it misapplies the distance formula.

Step 1: Start with the correct equation

We have the equation \( 20+6s = 8s \).

Step 2: Subtract \( 6s \) from both sides

Subtracting \( 6s \) from both sides gives \( 20+6s - 6s=8s - 6s \), which simplifies to \( 20 = 2s \).

Step 3: Solve for \( s \)

Divide both sides by 2: \( \frac{20}{2}=\frac{2s}{2} \), so \( s = 10 \).

Answer:

\( 20 + 6s = 8s \)

Second Sub - Question (Time Calculation)