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

Answer:

1. For the time - interval between 0.5 and 2: 4
2. For the time - interval between 1.5 and 2.5: 4

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$.

Step2: Find values for the interval 0.5 and 2

From the graph, when $x = 0.5$, $y\approx2$ and when $x = 2$, $y = 8$. Then $\frac{8 - 2}{2-0.5}=\frac{6}{1.5}=4$.

Step3: Find values for the interval 1.5 and 2.5

From the graph, when $x = 1.5$, $y = 6$ and when $x = 2.5$, $y = 10$. Then $\frac{10 - 6}{2.5 - 1.5}=\frac{4}{1}=4$.