Question

speed of runner
what is the runners average rate of change between the hours 0.5 and 2? mph
1.5 and 2.5? mph

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, the function represents the distance run as a function of time, and the average rate of change is the average speed.

Step2: Calculate average rate of change for the interval $[0.5,2]$

Let's assume from the graph that at $t = 0.5$, the distance $d_1$ is approximately $4$ miles and at $t = 2$, the distance $d_2$ is approximately $10$ miles. Then the average rate of change $\frac{d_2 - d_1}{2 - 0.5}=\frac{10 - 4}{1.5}=\frac{6}{1.5}=4$ mph.

Step3: Calculate average rate of change for the interval $[1.5,2.5]$

Assume from the graph that at $t = 1.5$, the distance $d_3$ is approximately $8$ miles and at $t = 2.5$, the distance $d_4$ is approximately $12$ miles. Then the average rate of change $\frac{d_4 - d_3}{2.5 - 1.5}=\frac{12 - 8}{1}=4$ mph.

Answer:

4 mph
4 mph