Question

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?

time elapsed (hours)	miles traveled (miles)
0.75	3.50
1.00	4.75

options:

• 4.75 miles per hour
• 5.00 miles per hour
• 5.50 miles per hour
• 6.00 miles per hour

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change (which is the average speed in this context) is given by the formula: $\text{Average Rate of Change} = \frac{\text{Change in Distance}}{\text{Change in Time}}$

Step2: Identify the values at the endpoints of the interval

For the interval from $t_1 = 0.75$ hours to $t_2 = 1.00$ hours:

• At $t_1 = 0.75$ hours, the distance $d_1 = 3.50$ miles.
• At $t_2 = 1.00$ hours, the distance $d_2 = 4.75$ miles.

Step3: Calculate the change in distance and change in time

• Change in distance: $\Delta d = d_2 - d_1 = 4.75 - 3.50 = 1.25$ miles.
• Change in time: $\Delta t = t_2 - t_1 = 1.00 - 0.75 = 0.25$ hours.

Step4: Calculate the average rate of change

Using the formula, $\text{Average Rate of Change} = \frac{\Delta d}{\Delta t} = \frac{1.25}{0.25} = 5.00$ miles per hour.

Answer:

5.00 miles per hour (corresponding to the option "5.00 miles per hour")