Problem:
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?
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Answer Choices:
A. Angela
B. Briana
C. Carla
D. Debra
E. Evelyn
Solution:
Evelyn covered more distance in less time than Briana, Debra and Angela, so her average speed is greater than any of their average speeds. Evelyn went almost as far as Carla in less than half the time that it took Carla, so Evelyn's average speed is also greater than Carla's.
The ratio of distance to time, or average speed, is indicated by the slope of the line from the origin to each runner's point in the graph. Therefore, the line from the origin with the greatest slope will correspond to the runner with the greatest average speed. Because Evelyn's line has the greatest slope, she has the greatest average speed.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions