Starting from 130 feet away, a person on bicycle rides towards a checkpoint and then passes it. The rider is traveling at a constant rate of

Question

25 feet per second. The distance between the bicycle and the checkpoint is given by the equationd = |130 - 25t|. At what times is the bike 15
feet away from the checkpoint?

Answer 1

To find the times when the bike is 15 feet away from the checkpoint, we can set up the equation:

|130 - 25t| = 15

We have two cases to consider: when 130 - 25t is positive and when it is negative.

1. When 130 - 25t is positive:
130 - 25t = 15
-25t = 15 - 130
-25t = -115
t = -115 / -25
t = 4.6 seconds

2. When 130 - 25t is negative:
-(130 - 25t) = 15
-130 + 25t = 15
25t = 15 + 130
25t = 145
t = 145 / 25
t = 5.8 seconds

Therefore, the bike is 15 feet away from the checkpoint at t = 4.6 seconds and t = 5.8 seconds.