Question

The graph below represents the speeds of Kael and Lynn as they run around a track.

A graph titled The Running Track. The horizontal axis shows time (minutes) and the vertical axis shows speed (m p h). Two lines begin at 0 speed in 0 minutes. The line labeled Lynn goes to 3 m p h in 8 minutes, to 12 m p h from 13 to 28 minutes, to 0 m p h in 40 minutes. The line labeled Kael goes to 10 m p h from 12 to 20 minutes, to 2 m p h in 32 minutes, to 0 m p h in 40 minutes.

For how many minutes did Lynn run at a greater speed than Kael?

12
17
23
28

Answer 1

28

Reason: For 12 ≤ t < 13, Lynn's speed is 3 + (9/5)(t − 8) which at t = 12 is 10.2 > Kael's 10. For 13 ≤ t ≤ 28, Lynn = 12 while Kael ≤ 10, so Lynn is faster. For 28 ≤ t < 32, 40 − t (Lynn) > 10 − (2/3)(t − 20) (Kael); for 32 ≤ t < 40, 40 − t > 10 − 0.25t. Thus Lynn runs faster than Kael for every minute from t = 12 up to t = 40, a total of 40 − 12 = 28 minutes.