Answered

  1. 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?

A2.3 sec and 5 sec
B1.6 sec and 5 sec
C2.3 sec and 4.6 sec
D1.6 sec and 4.6 sec

Verified Answer :

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.

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