AMC 8 2005 Problem 17

AMC8 2005 年第 17 题

行程问题★★★☆☆

The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?

越野队的训练结果如下图所示。则哪个学生的平均速度最高？

Distance | 距离

Time | 时间

A. $\text{Angela}$
B. $\text{Briana}$
C. $\text{Carla}$
D. $\text{Debra}$
E. $\text{Evelyn}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

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. OR OR 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: 𝐸 E .

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