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

2.3 sec and 5 sec

Explanation:

Answer 2

A. 2.3 sec and 5 sec

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=(70)/(30)` and
`(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.