AMC10 2009 A

AMC10 2009 A · Q4

AMC10 2009 A · Q4. It mainly tests Linear equations, Rates (speed).

Eric plans to compete in a triathlon. He can average 2 miles per hour in the 1-mile swim and 6 miles per hour in the 3-mile run. His goal is to finish the triathlon in 2 hours. To accomplish his goal what must his average speed, in miles per hour, be for the 15-mile bicycle ride?

Eric计划参加一场铁人三项比赛。他在1英里游泳中平均速度为2英里每小时，在3英里跑步中平均速度为6英里每小时。他的目标是在2小时内完成比赛。为了实现目标，他在15英里自行车骑行中的平均速度必须是多少英里每小时？

(A) $\frac{120}{11}$ $\frac{120}{11}$

(B) 11 11

(D) $\frac{45}{4}$ $\frac{45}{4}$

(E) 12 12

Answer

Correct choice: (A)

正确答案：（A）

Solution

Eric can complete the swim in $\frac{1}{2} = \frac{1}{4}$ hour. He can complete the run in $\frac{3}{6} = \frac{1}{2}$ hour. This leaves $2 - \frac{1}{4} - \frac{1}{2} = \frac{11}{8}$ hours to complete the bicycle ride. His average speed for the ride must be $\frac{15}{\frac{11}{8}} = \frac{120}{11}$ miles per hour.

Eric完成游泳需要 $\frac{1}{2} = \frac{1}{4}$ 小时。完成跑步需要 $\frac{3}{6} = \frac{1}{2}$ 小时。这剩下 $2 - \frac{1}{4} - \frac{1}{2} = \frac{11}{8}$ 小时来完成自行车骑行。他的骑行平均速度必须是 $\frac{15}{\frac{11}{8}} = \frac{120}{11}$ 英里每小时。

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