Question

一名铁人三项运动员参加一场比赛，其中游泳、骑车和跑步三段距离相同。他游泳速度为每小时 $3$ 千米，骑车速度为每小时 $20$ 千米，跑步速度为每小时 $10$ 千米。以下哪一项最接近他整场比赛的平均速度，单位为千米/小时？

A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of $3$ kilometers per hour, bikes at a rate of $20$ kilometers per hour, and runs at a rate of $10$ kilometers per hour. Which of the following is closest to the triathlete's average speed, in kilometers per hour, for the entire race?

$3$

$4$

$5$

$6$

$7$

答案：D

知识点：路程、速度与时间调和平均数

难度评级：1100

解答：

设每段长为 $x$ 。总距离为 $3x$ ，总时间为 $\dfrac{x}{3} + \dfrac{x}{20} + \dfrac{x}{10} = \dfrac{29}{60}x$ 小时。

平均速度为 $\dfrac{3x}{\frac{29}{60}x} = \dfrac{180}{29} \approx 6.2$ ，最接近 $6$ 。

所以正确答案是 D。

Let each segment have length $x.$ The total time is $\dfrac{x}{3} + \dfrac{x}{20} + \dfrac{x}{10} = \dfrac{29}{60}x$ hours for the distance $3x.$

The average speed is $\dfrac{3x}{\frac{29}{60}x} = \dfrac{180}{29} \approx 6.2,$ which is closest to $6.$

Thus, the correct answer is D.

2008 AMC 10A 第 6 题

答案：D

难度评级：1100

解答：

其他年份的第 6 题