Question

The graph relates the distance traveled (in miles) to the time elapsed (in hours) on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?

first $(0\text{-}1)$

second $(1\text{-}2)$

third $(2\text{-}3)$

ninth $(8\text{-}9)$

last $(11\text{-}12)$

Solution:

The average speed during any single hour equals the distance the airplane covers in that hour, which on the graph is the vertical rise of the curve over that one-hour interval. So the largest average speed happens during the hour where the curve is steepest.

From $t=1$ to $t=2$ the curve climbs from about $500$ miles to about $1000$ miles, a rise of roughly $500$ miles, giving an average speed near $500$ mph. During every other hour the curve rises by less than $350$ miles, so those average speeds are all smaller. The steepest climb, and hence the largest average speed, is during the second hour.

Thus, the correct answer is B .

1990 AMC 8 Problem 23

Solution:

Problem 23 in Other Years