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 $\rightarrow \boxed{\text{B}}$.

See Also

1990 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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All AJHSME/AMC 8 Problems and Solutions
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