Question

Find the rate of change.

Time(hours)
4

6

8

10

Distance (miles)
252

378

504

630
answers below:
1/63; The car travels 1 mile every 63 hours.

10; The car travels 1 mile every 63 hours

63/1; The car travels 63 miles every 1 hour.

252; The car travels 252 miles.

Answer 1

To find the rate of change of distance with respect to time, we can use the given values of time and distance.

Let's check the values:

- At 4 hours, the distance is 252 miles.
- At 6 hours, the distance is 378 miles.
- At 8 hours, the distance is 504 miles.
- At 10 hours, the distance is 630 miles.

Now, we can calculate the distance traveled per hour from the data:

1. From 4 to 6 hours:
\[
\text{Distance change} = 378 - 252 = 126 \text{ miles}
\]
\[
\text{Time change} = 6 - 4 = 2 \text{ hours}
\]
\[
\text{Rate of change} = \frac{126 \text{ miles}}{2 \text{ hours}} = 63 \text{ miles per hour}
\]

2. From 6 to 8 hours:
\[
\text{Distance change} = 504 - 378 = 126 \text{ miles}
\]
\[
\text{Time change} = 8 - 6 = 2 \text{ hours}
\]
\[
\text{Rate of change} = \frac{126 \text{ miles}}{2 \text{ hours}} = 63 \text{ miles per hour}
\]

3. From 8 to 10 hours:
\[
\text{Distance change} = 630 - 504 = 126 \text{ miles}
\]
\[
\text{Time change} = 10 - 8 = 2 \text{ hours}
\]
\[
\text{Rate of change} = \frac{126 \text{ miles}}{2 \text{ hours}} = 63 \text{ miles per hour}
\]

The rate of change remains consistent at 63 miles per hour across the intervals.

Therefore, the best match from your options is:
**63/1; The car travels 63 miles every 1 hour.**