Chapter 3, Problem 78SGR

To determine

The absolute value function for the J’s distance and time to reach flagpole.

Answer to Problem 78SGR

The absolute value function for the J’s distance and time to reach flagpole are $\text{Distance}=\left|1500-500x\right|$ and $3\text{}\text{}\text{mins}$ respectively.

Explanation of Solution

Given:

The Speed of J’s is $500\text{ft/min}$ .

Initial distance from the flagpole is $1500\text{ft}$ .

Calculation:

Consider the time x minutes.

Distance at time x is calculated as follows:

  $\begin{array}{c}D=\text{Speed}\times \text{time}\\ =500x\end{array}$

As the J approaches towards flagpole, the distance between then decrease by the amount $1500-500x$ .

Distance can never be negative, and then the required absolution function is expressed as follows:

  $\text{Distance}=\left|1500-500x\right|$

Time to reach the flagpole is calculated as follows:

  $\begin{array}{c}\left|1500-500x\right|=0\\ x=\frac{1500}{500}\\ =3\text{}\text{}\text{mins}\end{array}$

Thus, the absolute value function for the J’s distance and time to reach flagpole are $\text{Distance}=\left|1500-500x\right|$ and $3\text{}\text{}\text{mins}$ respectively.