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? Choices: (A)20s + 6 = 8s (B)20 + 6s = 8s How long will it take for Billy to catch up to Reggie? Simplify any fractions. ____ seconds

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?   Choices: (A)20s + 6 = 8s (B)20 + 6s = 8s  How long will it take for Billy to catch up to Reggie? Simplify any fractions.   ____ seconds

Bytelearn · Accepted Answer

Set Up Problem: Let's set up the problem. We know that Reggie starts 20 meters ahead and runs at 6 meters per second. Billy runs at 8 meters per second. We want to find the time s when the distance Billy runs equals the distance Reggie runs plus the 20-meter head start.Calculate Distances: The distance that Billy runs can be represented as 8s, since he runs at 8 meters per second for s seconds. The distance that Reggie runs can be represented as 6s, since he runs at 6 meters per second for s seconds. However, since Reggie starts 20 meters ahead, we need to add 20 to his distance.Formulate Equation: The correct equation to represent the situation where Billy catches up to Reggie is the distance Billy runs (8s) equals the distance Reggie runs (6s) plus the 20-meter head start. So the equation is 8s = 6s + 20.Isolate Variable: Now we need to solve for s. We can do this by subtracting 6s from both sides of the equation to isolate s on one side. 8s - 6s = 6s + 20 - 6s 2s = 20Find Solution: To find the value of s, we divide both sides of the equation by 2. 2s / 2 = 20 / 2 s = 10

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