Question

Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.

A coordinate grid labeled Distances Traveled with Time in minutes along the horizontal x-axis and Distance in miles along the vertical y-axis with 2 lines. The first line is labeled y equals (StartFraction 1 over 15 EndFraction) x plus 5 and passes through (0, 5) and (60, 9). The second line is labeled y equals (StartFraction 2 over 15 EndFraction) x. The lines appear to intersect at between 70 and 80 along the x-axis and 10 on the y-axis.
How many minutes does it take Arnob to catch up to Kathleen?

9.8
10
73.5

75

Answer 1

Set their distances equal: (1/15)x + 5 = (2/15)x.
So 5 = (1/15)x, hence x = 5·15 = 75 minutes.