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

Bytelearn · Accepted Answer

Set Up Equation: To find the correct equation, we need to set up an equation that represents the distance each brother will run. Since Reggie starts 20 meters ahead, we can represent his head start as 20 meters. Billy's distance will be the distance Reggie runs plus the 20 meters head start. We can use the formula distance = speed × time. For Billy, the distance is 8 meters per second times the number of seconds (s), and for Reggie, it is 20 meters plus 6 meters per second times the number of seconds (s).Equal Distances Equation: The correct equation that represents the moment Billy catches up to Reggie is when the distances they have run are equal. This gives us the equation 8s = 20 + 6s.Isolate Variable: To solve for s, we need to isolate the variable on one side of the equation. We can do this by subtracting 6s from both sides of the equation to get 2s = 20.Divide to Solve: Now, we divide both sides of the equation by 2 to solve for s. This gives us s = 20 / 2.Final Answer: Performing the division, we find that s = 10. This means it will take Billy 10 seconds to catch up to Reggie.

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