Question

Find the rate of change. Time(hours) Distance (miles)4 2526 3788 50410 630(1 point)Responses163; The car travels 1 mile every 63 hours.1 63 ; The car travels 1 mile every 63 hours.10; The car travels 1 mile every 63 hours10; The car travels 1 mile every 63 hours631; The car travels 63 miles every 1 hour.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 look at the distance traveled over various time intervals.

We can make use of the data you provided:

1. At 4 hours, the car has traveled 25 miles.
2. At 6 hours, the car has traveled 37 miles.
3. At 8 hours, the car has traveled 50 miles.
4. At 10 hours, the car has traveled 63 miles.

Now, let's calculate the rate of change (speed) between these points:

1. From 4 hours to 6 hours:
- Change in distance = 37 miles - 25 miles = 12 miles
- Change in time = 6 hours - 4 hours = 2 hours
- Rate of change = \( \frac{12 \text{ miles}}{2 \text{ hours}} = 6 \text{ miles per hour} \)

2. From 6 hours to 8 hours:
- Change in distance = 50 miles - 37 miles = 13 miles
- Change in time = 8 hours - 6 hours = 2 hours
- Rate of change = \( \frac{13 \text{ miles}}{2 \text{ hours}} = 6.5 \text{ miles per hour} \)

3. From 8 hours to 10 hours:
- Change in distance = 63 miles - 50 miles = 13 miles
- Change in time = 10 hours - 8 hours = 2 hours
- Rate of change = \( \frac{13 \text{ miles}}{2 \text{ hours}} = 6.5 \text{ miles per hour} \)

The rate of change seems to vary slightly but is approximately 6 to 6.5 miles per hour.

Now, regarding your responses:

- The statements "The car travels 63 miles every 1 hour." and "The car travels 1 mile every 63 hours." seem to be incorrect given our calculations.

None of your provided responses directly reflect the average speed we found (which ranges from 6 to 6.5 miles per hour).

If you have the specific response options outlined and would like feedback on those, please clarify that, and I’d be happy to assist!