Chapter 1.4, Problem 45E

To determine

the time when the distance of the car from you is 60 feet.

Answer to Problem 45E

After 5 seconds and then again after 7.5 seconds.

Explanation of Solution

Consider the given equation:

  $d=\left|300-48t\right|$

Now substitute $d=60$

  $\begin{array}{c}\left|300-48t\right|=60\\ 300-48t=\pm 60\end{array}$

Now,

  $\begin{array}{c}300-48t=60\\ 300-60=48t\\ 240=48t\end{array}$

  $\begin{array}{c}\frac{240}{48}=t\\ 5=t\end{array}$

Or

  $\begin{array}{c}300-48t=-60\\ 300+60=48t\\ 360=48t\end{array}$

  $\begin{array}{c}\frac{360}{48}=t\\ 7.5=t\end{array}$

Check:

  $\begin{array}{c}60=\left|300-48\left(5\right)\right|\\ 60=\left|300-240\right|\\ 60=\left|60\right|\\ 60=60\end{array}$

And

  $\begin{array}{c}60=\left|300-48\left(7.5\right)\right|\\ 60=\left|300-360\right|\\ 60=\left|-60\right|\\ 60=60\end{array}$

Both the statements are true.

Conclusion:

The distance of the car from you is 60 feet once arter 5 seconds and then again after 7.5 seconds.