AMC10 2008 A

AMC10 2008 A · Q6

AMC10 2008 A · Q6. It mainly tests Rates (speed), Arithmetic misc.

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?

一名铁人三项运动员参加了一场铁人三项比赛，其中游泳、骑行和跑步段的长度相同。该运动员游泳速度为3千米/小时，骑行速度为20千米/小时，跑步速度为10千米/小时。以下哪一项最接近该运动员整个比赛的平均速度（千米/小时）？

(A) 3 3

(B) 4 4

(D) 6 6

(E) 7 7

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let $x$ be the length of one segment, in kilometers. To complete the race, the triathlete takes $$\frac{x}{3}+\frac{x}{20}+\frac{x}{10}=\frac{29}{60}x$$ hours to cover the distance of $3x$ kilometers. The average speed is therefore $$\frac{3x}{\frac{29}{60}x}\approx 6\ \text{kilometers per hour}.$$

答案（D）：设 $x$ 为一段的长度（单位：千米）。要完成比赛，该铁人三项运动员用时 $$\frac{x}{3}+\frac{x}{20}+\frac{x}{10}=\frac{29}{60}x$$ 小时跑完 $3x$ 千米。因此平均速度为 $$\frac{3x}{\frac{29}{60}x}\approx 6\ \text{千米/小时}.$$

Topics