Since the distance traveled in `13` minutes is `4.12` miles, the average speed is `0.317` miles per minute, or just over `19` mph. In Figure A1 we repeat Figure C1 with labels on the vertical axis and a horizontal line at `v=0.317`. The area of the rectangle under this line is `0.317 times 13 ~~ 4.12`, or the same as the total distance traveled. A good guess is that this area is exactly the same as the area under the curve. You can see that the two areas are approximately equal by counting rectangles and parts of rectangles in the shaded parts of the figure. Later in this section we will see why the two areas are exactly the same.

Figure A1   Actual speed and average speed (miles per minute)