Question

The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?

A. 2/5

B. 1

C.2

D.5/2

Answer 1

Hence, option D is correct.

(i.e. Average speed is 5/2 miles/hour)

Explanation:

We are asked to find the average rate of speed over the interval [9, 11].

We know that average speed is given as the ratio of total distance over total time.

the distance when time=9 hours is 6 miles.

and the distance when time=11 hours is 11 miles.

Hence, average speed is given as:

`Average speed=(Total distance)/(Total time)\\\\Average speed=(11-6)/(11-9)\\\\Average speed=(5)/(2)`

Hence average speed is 5/2 miles/hour.

Answer 2

For this case what you should see is that for the interval [9, 11] the behavior of the function is almost linear.
Therefore, we can find the average rate of change as follows:
m = (y2-y1) / (x2-x1)
m = (11-6) / (11-9)
m = (5) / (2)
m = 5/2
Answer:
the average rate of speed over the interval [9, 11] is:
D. 5 / 2