Question

9. start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a constant rate of 30 feet per second. the distance between the bicycle and the checkpoint is given by the equation d=|110-3t|. at what times is the bike 40 feet away from the checkpoint?
A. 2.3 sec and 5 sec
B. 1.6 sec and 5 sec
C. 2.3 sec and 4.6 sec
D. 1.6 sec and 4.6 sec

Answer 1

Answer:

A. 2.3 sec and 5 sec

Step-by-step explanation:

We are given that start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a constant rate of 30 feet per second.

The distance between the bicycle and the checkpoint is given by the equation :

$d=|110-30t|$

Now we are required to calculate at what times is the bike 40 feet away from the checkpoint. So, substitute d = 40 in the equation

$40=|110-30t|$

$40=110-30t$     and    $40= -110+30t$

$30t=110-40t$     and   $40+110=30t$

$30t=70$               and   $150=30t$

$t=\frac{70}{30}$                   and   $\frac{150}{30}=t$

$t=2.3$                  and   $5=t$

Hence at 2.3 sec and 5 sec  the bike is 40 feet away from the checkpoint.