Chapter 3, Problem 78SGR

To determine

To find: Absolute value function that models John’s distance from the flag pole and time to reach flag pole.

Answer to Problem 78SGR

Absolute value function that models John’s distance from flag pole after $x$ minutes is $T\left(x\right)=\left|1500-500x\right|$

Time required to reach flag pole is 3 Minutes.

Explanation of Solution

Given information:

Speed of john = $500ft/\min$

Initial Distance of John form flag pole = 1500 ft.

John is moving towards Flag pole.

From given information

Speed of john = $500ft/\min$

  $1$ min $\to -500ft$

Negative sign because John is moving towards Flag pole.

Multiplying with $x$ on both sides

We get

  $\begin{array}{l}1\times x\to -500\times x\\ \Rightarrow x\to -500x\end{array}$

Therefore

For $x$ minutes John will travel $-500x$ feet

Total distance = distance travelled in $x$ minutes + Initial distance

Let $T\left(x\right)$ be Total distance.

  $\Rightarrow T\left(x\right)=1500-500x$

As distance cannot be negative so we need to make it absolute value function

  $\Rightarrow T\left(x\right)=\left|1500-500x\right|$

Therefore,

Absolute value function that models John’s distance from flag pole after $x$ minutes is $T\left(x\right)=\left|1500-500x\right|$

To calculate time to reach flag pole we need to make $T\left(x\right)=0$

Because when john reached flag pole the distance will become Zero.

  $\begin{array}{l}T\left(x\right)=\left|1500-500x\right|\\ \Rightarrow 0=\left|1500-500x\right|\\ \Rightarrow 1500-500x=0\\ \Rightarrow 500x=1500\\ \Rightarrow x=\frac{1500}{500}\\ \Rightarrow x=3\end{array}$

Therefore

Time required to reach flag pole is 3 Minutes.