Question

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
(1 point)
The lines in option #___
can be used to determine when Ella catches up with her mother.

Answer 1

Option #1.

Reason: Set 4x = 6x - 12. Solving gives 2x = 12 → x = 6 hours (since Brandi's start). Distance y = 4(6) = 24 miles. So after 6 hours (Brandi's time), Ella catches up at 24 miles.