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The question is asking to determine the average rate of change, in miles per hour (mi/hr), between hour 2 and hour 7 of a family's trip. We are also asked to explain what this rate of change means.

From the table:

- At hour 2, the distance is 140 miles.
- At hour 7, the distance is 480 miles.

### Step-by-step solution:

1. **Formula for average rate of change**:
   \[
   \text{Average rate of change} = \frac{\text{Change in distance}}{\text{Change in time}}
   \]

2. **Apply the values**:
   - Change in distance = \( 480 \, \text{miles} - 140 \, \text{miles} = 340 \, \text{miles} \)
   - Change in time = \( 7 \, \text{hours} - 2 \, \text{hours} = 5 \, \text{hours} \)

3. **Calculate the average rate of change**:
   \[
   \text{Average rate of change} = \frac{340 \, \text{miles}}{5 \, \text{hours}} = 68 \, \text{mi/hr}
   \]

### Explanation:
The average rate of change of 68 mi/hr means that between hour 2 and hour 7, the family was traveling at an average speed of 68 miles per hour.

Would you like further clarification on this? Here are some related questions for deeper exploration:

1. What is the meaning of the average rate of change in real-world situations like this one?
2. How does the concept of average speed differ from instantaneous speed?
3. Could the rate of change be constant, or is it likely that it varies over time?
4. What would the average rate of change be between hour 0 and hour 7?
5. How would you calculate the total distance traveled using this rate of change?

### Tip:
The average rate of change can be interpreted as the slope of a line connecting two points on a distance-time graph. In this case, it represents the family's average speed over the time interval.

Determine the average rate of change, in mi/hr, between hour 2 and hour 7. Explain what this rate of change means as it relates to the family's trip.

Learn how to calculate the average rate of change in miles per hour between hour 2 and hour 7 of a family's trip. Understand how to apply the formula for rate of change and interpret what it means in real-world contexts. Suitable for students in Grades 6-8.

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