College

A truck driver makes deliveries across the country. He records the number of miles he has traveled in relation to the time driven, as shown in the table below.

[tex]
\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Time \\
(hours)
\end{tabular} & 7 & 9 & 11 & 13 & 15 \\
\hline
\begin{tabular}{c}
Distance \\
(miles)
\end{tabular} & 420 & 540 & 660 & 780 & 900 \\
\hline
\end{tabular}
\]
[/tex]

What is the rate of change for the information in the table?

A. 64 miles per hour
B. 68 miles per hour
C. 60 miles per hour
D. 56 miles per hour

Answer :

To find the rate of change for the information in the table, we need to calculate the average speed of the truck driver in miles per hour.

The table provides us with:

- Time (hours): 7, 9, 11, 13, 15
- Distance (miles): 420, 540, 660, 780, 900

The rate of change, or average speed, can be calculated using the formula:

[tex]\[ \text{Rate of Change} = \frac{\text{Change in Distance}}{\text{Change in Time}} \][/tex]

Let's calculate this step by step:

1. Identify the initial and final data points:
- Initial time: 7 hours
- Final time: 15 hours
- Initial distance: 420 miles
- Final distance: 900 miles

2. Calculate the change in distance:
[tex]\[ \text{Change in Distance} = 900 \text{ miles} - 420 \text{ miles} = 480 \text{ miles} \][/tex]

3. Calculate the change in time:
[tex]\[ \text{Change in Time} = 15 \text{ hours} - 7 \text{ hours} = 8 \text{ hours} \][/tex]

4. Compute the rate of change:
[tex]\[ \text{Rate of Change} = \frac{480 \text{ miles}}{8 \text{ hours}} = 60 \text{ miles per hour} \][/tex]

Therefore, the rate of change is 60 miles per hour. The correct answer is:

C. 60 miles per hour

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