Question

Starting from 130 feet away, a person on bicycles 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 equation d=|130-25d|. 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 need to solve the equation:

d = |130 - 25t| = 15

First, let's consider the case when 130 - 25t is positive:

130 - 25t = 15
-25t = -115
t = 4.6

In this case, when t = 4.6, the bike is 15 feet away from the checkpoint.

Now, let's consider the case when 130 - 25t is negative:

-(130 - 25t) = 15
-130 + 25t = 15
25t = 145
t = 5.8

In this case, when t = 5.8, the bike is also 15 feet away from the checkpoint.

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