The table shows how far a distance runner has traveled since the race began. What is her average rate of change, in miles per hour, during the interval 0.75 to 1.00 hours?
To determine the average rate of change in miles per hour during the interval from 0.75 to 1.00 hours, we can follow these steps:
1. Identify the given data points: - At [tex]\( t = 0.75 \)[/tex] hours, the distance traveled is [tex]\( 3.50 \)[/tex] miles. - At [tex]\( t = 1.00 \)[/tex] hours, the distance traveled is [tex]\( 4.75 \)[/tex] miles.
2. Use the formula for the average rate of change: [tex]\[
\text{Average rate of change} = \frac{\Delta \text{Distance}}{\Delta \text{Time}}
\][/tex] Where [tex]\(\Delta\)[/tex] represents the change in the respective quantities.
3. Calculate [tex]\(\Delta \text{Distance}\)[/tex] and [tex]\(\Delta \text{Time}\)[/tex]: - Change in Distance ([tex]\(\Delta \text{Distance}\)[/tex]): [tex]\[
\Delta \text{Distance} = \text{Distance at } t = 1.00 \text{ hours} - \text{Distance at } t = 0.75 \text{ hours}
\][/tex] [tex]\[
\Delta \text{Distance} = 4.75 \text{ miles} - 3.50 \text{ miles} = 1.25 \text{ miles}
\][/tex]
