Question

the table shows the distance a runner has traveled y, in miles, x minutes after the start of a race. what is the runners average rate of change, in miles per minute, from 60 to 120 minutes?

time (min)	distance (miles)
30	3.48
60	6.42
90	9.18
120	12.0

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x_1 = 60$, $x_2=120$, $y_1 = 6.42$ and $y_2 = 12.0$.

Step2: Substitute values into formula

$\frac{\Delta y}{\Delta x}=\frac{12.0 - 6.42}{120 - 60}$.

Step3: Calculate numerator and denominator

The numerator is $12.0-6.42 = 5.58$, and the denominator is $120 - 60=60$.

Step4: Compute the result

$\frac{5.58}{60}=0.093$.

Answer:

$0.093$