To determine when Ella catches up with her mother, we need to look at the linear equations that model their respective distances based on time.
Brandi starts hiking two hours earlier and has a pace of 4 mph. So her distance can be represented by:
- Brandi's Distance (y): \( y = 4(x + 2) \), where \( x \) is the time in hours that Ella has been hiking (since she starts 2 hours later).
Ella starts two hours after her mother and hikes at a pace of 6 mph. Her distance can be represented by:
- Ella's Distance (y): \( y = 6x \), where \( x \) is the time in hours since she started hiking.
To visualize this on a graph, we can plot these two equations. The point where the two lines intersect will show the time and distance when Ella catches up with Brandi.
Given the options, you would select the lines that correspond to the distances from both Brandi and Ella. Therefore, the correct option would represent the lines for Brandi and Ella.
Without seeing the specific lines labeled as Line 1, Line 2, Line 3, and Line 4, it is challenging to select the exact option. However, it should include the line for Brandi's model and the line for Ella's model.
Please choose Option #1: Line 1 and Line 2, as it typically would represent the two hikers' distances. However, if you can clarify which lines correspond to those equations visually, I could more confidently identify the correct option for you.