Chapter 3, Problem 57SGR

To determine

To find: Equation that represents given table and time for sound to travel 72300 feet.

Answer to Problem 57SGR

Equation that represents given table is $y=4820x$ .

Time for sound to travel distance of 72300 is 15 seconds.

Explanation of Solution

Given information:

Distance = 72300 feet

Concept:

When two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given

Slope = $m=\frac{y_2-y_1}{x_2-x_1}$

Equation of that line is

  $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$

We can take any two points from the table to find equation.

Taking first two points from the given table

  $x$ -coordinate as time and $y$ -coordinate as distance.

We get

points are

  $\begin{array}{l}\left(x_1,y_1\right)=\left(1,4820\right)\\ \left(x_2,y_2\right)=\left(2,9640\right)\end{array}$

Equation of the line is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \Rightarrow y-4820=\left(\frac{9640-4820}{2-1}\right)\left(x-1\right)\\ \Rightarrow y-4820=\left(4820\right)\left(x-1\right)\\ \Rightarrow y-4820=4820x-4820\\ \Rightarrow y=4820x-4820+4820\\ \Rightarrow y=4820x\end{array}$

Therefore

Equation that represents given table is $y=4820x$ .

Given

Distance = 72300

It means $y=72300$

On substituting value of $y=72300$ in above equation

We get

  $\begin{array}{l}y=4820x\\ \Rightarrow 72300=4820x\\ \Rightarrow x=\frac{72300}{4820}\\ \Rightarrow x=15\end{array}$

Therefore, time for sound to travel distance of 72300 is 15 seconds.