You start driving away from Morgantown at 12:00. Your distance away $t$ hours after you left is given by $f(t)$. Find your average speed from 2:00 to 5:00.
$\begin{array}{ccccccc}x & 0 & 1 & 2 & 3 & 4 & 5 \\ f(x) & 0 & 51 & 163 & 216 & 275 & 351\end{array}$
The average rate of change is
Answer
Final Answer: The average speed from 2:00 to 5:00 is \(\boxed{62.67}\) miles per hour.
Step 1 ：The distance at 2:00 is 163 miles and the distance at 5:00 is 351 miles.
Step 2 ：The total distance traveled from 2:00 to 5:00 is calculated by subtracting the distance at 2:00 from the distance at 5:00, which is \(351 - 163 = 188\) miles.
Step 3 ：The total time from 2:00 to 5:00 is 3 hours.
Step 4 ：The average speed is calculated by dividing the total distance traveled by the total time, which is \(\frac{188}{3} = 62.67\) miles per hour.
Step 5 ：Final Answer: The average speed from 2:00 to 5:00 is \(\boxed{62.67}\) miles per hour.
