Brandi and her daughter, Ella, are training for a hiking challenge. Because Brandi hikes at a slower pace than her daughter, she begins the practice hike two hours earlier. If Brandi averages a pace of 4 mph, the linear equation y=4x
can be used to model her distance, y, in miles with respect to her time, x, in hours. If Ella averages a pace of 6 mph and begins two hours after her mom, the linear equation y=6x−12
can be used to model her distance, y, in miles with respect to time, x, in hours. The graph of which two lines can be used to find the time and distance when Ella catches up with her mother?
Option #1: Line 1 and Line 2
Option #2: Line 2 and Line 3
Option #3: Line 3 and Line 4
Option #4: Line 1 and Line 4
Option #1: Line 1 and Line 2
The equations for Brandi and Ella's distances are y=4x and y=6x-12, respectively. When Ella catches up with Brandi, their distances will be equal. Therefore, we can set the two equations equal to each other:
4x = 6x - 12
2x = 12
x = 6
So, they will meet after 6 hours of hiking. To find the distance, we can plug this x value back into one of the equations:
Brandi's distance: y = 4(6) = 24 miles
Ella's distance: y = 6(6) - 12 = 24 miles
Therefore, Ella will catch up with Brandi after 6 hours of hiking, when they are both 24 miles into their hike.