Question

Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice’s race?

Antonio’s Distance Past the Landmark
Time (seconds)
8
12
16
20
24
Distance (meters)
29
41
53
65
77

A graph titled Candice's Distance Past the Landmark has time (seconds) on the x-axis, and Distance (meters) on the y-axis. A line goes through points (5, 22), (10, 42), (15, 62) and (20, 82).
Antonio had a head start of 1 meter.
Antonio had a head start of 3 meters.
Candice had a head start of 1 meter.
Candice had a head start of 3 meters.

Answer 1

Antonio: slope = (41−29)/(12−8) = 12/4 = 3, so D_A(t)=3t+b. Using (8,29): 24+b=29 ⇒ b=5.

Candice: slope = (42−22)/(10−5)=20/5=4, so D_C(t)=4t+b. Using (5,22): 20+b=22 ⇒ b=2.

At t=0 Antonio is 5 m past the landmark and Candice is 2 m past it, so Antonio had a 3-meter head start.