Question

The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.


10; your car travels for 10 hours.



260; your car travels 260 miles.

Answer 1

To find the rate of change in the given scenario, we need to determine how the distance your car travels changes with respect to time. The data provided shows:

- Time: 10 hours
- Distance: 260 miles

### Step 1: Calculate the Rate of Change

To find the rate of change (usually represented as \( r \)), we can use the formula:

\[
r = \frac{\text{Change in distance}}{\text{Change in time}}
\]

In this case, the change in distance is 260 miles (the total distance traveled), and the change in time is 10 hours.

Substituting these values into the formula, we get:

\[
r = \frac{260 \text{ miles}}{10 \text{ hours}} = 26 \text{ miles per hour}
\]

### Step 2: Interpret the Rate of Change

The rate of change of 26 miles per hour means that your car is traveling at a consistent speed of 26 miles for every hour of travel time. This rate indicates that if you travel for 5 hours, you would cover:

\[
5 \text{ hours} \times 26 \text{ miles per hour} = 130 \text{ miles}
\]

Similarly, if you traveled for 3 hours, you would cover:

\[
3 \text{ hours} \times 26 \text{ miles per hour} = 78 \text{ miles}
\]

Thus, the rate of change reflects the speed of your car, providing an understanding of how far you can expect to travel over a period of time based on this constant speed. This consistent rate can help in planning trips, estimating arrival times, and managing fuel efficiency.