Example 3 from Precalculus, 1.3 Rates of Change and Behavior of Graphs

Computing Average Rate of Change from a Table

After picking up a friend who lives 10 miles away, Anna records her distance from home over time. The values are shown in Table 2. Find her average speed over the first 6 hours.

t (hours)	0	1	2	3	4	5	6	7
D(t) (miles)	10	55	90	153	214	240	292	300

Table 2

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Here, the average speed is the average rate of change. She traveled 282 miles in 6 hours, for an average speed of

$\begin{array}{l} \begin{array}{l} \frac{292 - 10}{6 - 0} = \frac{282}{6} \end{array} \\ = 47 \end{array}$
The average speed is 47 miles per hour.

How did it go?

Solution