# 1990 AJHSME Problems/Problem 23

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## Problem

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?

$[asy] unitsize(12); for(int a=1; a<13; ++a) { draw((2a,-1)--(2a,1)); } draw((-1,4)--(1,4)); draw((-1,8)--(1,8)); draw((-1,12)--(1,12)); draw((-1,16)--(1,16)); draw((0,0)--(0,17)); draw((-5,0)--(33,0)); label("0",(0,-1),S); label("1",(2,-1),S); label("2",(4,-1),S); label("3",(6,-1),S); label("4",(8,-1),S); label("5",(10,-1),S); label("6",(12,-1),S); label("7",(14,-1),S); label("8",(16,-1),S); label("9",(18,-1),S); label("10",(20,-1),S); label("11",(22,-1),S); label("12",(24,-1),S); label("Time in hours",(11,-2),S); label("500",(-1,4),W); label("1000",(-1,8),W); label("1500",(-1,12),W); label("2000",(-1,16),W); label(rotate(90)*"Distance traveled in miles",(-4,10),W); draw((0,0)--(2,3)--(4,7.2)--(6,8.5)); draw((6,8.5)--(16,12.5)--(18,14)--(24,15)); [/asy]$

$\text{(A)}\ \text{first (0-1)} \qquad \text{(B)}\ \text{second (1-2)} \qquad \text{(C)}\ \text{third (2-3)} \qquad \text{(D)}\ \text{ninth (8-9)} \qquad \text{(E)}\ \text{last (11-12)}$

## Solution

The time when the average speed is greatest is when the slope of the graph is steepest. This is in the second hour $\rightarrow \boxed{\text{B}}$.