1959 AMC 12 第 30 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

30.

AA 跑完一圈圆形跑道需 4040 秒。BB 沿相反方向跑,每隔 1515 秒与 AA 相遇一次。BB 跑完一圈需多少秒?

AA can run around a circular track in 4040 seconds. B,B, running in the opposite direction, meets AA every 1515 seconds. What is BB’s time to run around the track, expressed in seconds?

121212\dfrac12

2424

2525

271227\dfrac12

5555

答案:B
知识点:相对速度速率
难度评级:1140
小提示:

用每秒多少圈表示两人的速度

Measure each runner’s speed in laps per second

大提示:

因为两人方向相反,所以速度之和为每秒 115\frac{1}{15}

Because they run in opposite directions, their speeds add to 115\frac{1}{15} lap per second

解答:

BB 跑一圈的时间为 tt,则两人的相对速度为 140+1t=115 \frac1{40}+\frac1t=\frac1{15}\text{。}因此 1t=124\frac{1}{t}=\frac{1}{24},所以 t=24t=24 秒。

因此,正确答案是 B

If BB’s lap time is t,t, their relative speed is 140+1t=115. \frac1{40}+\frac1t=\frac1{15}. Thus 1t=124,\frac{1}{t}=\frac{1}{24}, so t=24t=24 seconds.

Therefore, the correct answer is B.

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