8. Kaplee drove her scooter at an average speed of 15 miles per hour and was 5 miles ahead of Sophia. Sophia drove her scooter at an average speed of 20 miles per hour. This situation can be represented with the system \( y=15 x+5 \) and \( y=20 x \), where \( x \) is the nurmber of hours and is the number of miles from the starting point. After how many hours are kaylee and sophia the same distance from the starting point?

To determine after how many hours Kaylee and Sophia will be the same distance from the starting point, let's analyze the given information using the provided equations. ### Given: - **Kaylee's Distance:** \( y = 15x + 5 \) - *15 miles per hour* is her speed. - She has a *5-mile head start*. - **Sophia's Distance:** \( y = 20x \) - *20 miles per hour* is her speed. Here, \( x \) represents the number of hours, and \( y \) represents the distance from the starting point. ### Setting the Equations Equal: To find when both are the same distance from the start, set Kaylee's distance equal to Sophia's distance: \[ 15x + 5 = 20x \] ### Solving for \( x \): 1. **Subtract \( 15x \) from both sides:** \[ 5 = 5x \] 2. **Divide both sides by 5:** \[ x = 1 \] ### Conclusion: After **1 hour**, Kaylee and Sophia will be at the same distance from the starting point. **Answer:** After 1 hour, Kaylee and Sophia are the same distance from the starting point.