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
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?
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.