1962 AMC 12 第 35 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。
35.
某人在下午 刚过不久外出赴宴时，看到手表的时针与分针成 角。他在下午 前返回时，发现两根指针再次成 角。他离开的分钟数为：
A man on his way to dinner shortly after p.m. observes that the hands of his watch form an angle of Returning before p.m. he notices that again the hands of his watch form an angle of The number of minutes that he has been away is:
小提示：
在这段时间内，分针每分钟比时针多转
During the interval, the minute hand gains on the hour hand at per minute
大提示：
两次观察之间，带符号的角度差从 变为
Between the two observations, the signed separation changes from to
解答：
两次观察分别位于两针重合时刻的前后两侧。带符号的角度差变化了 。由于分针每分钟比时针多转 ，所以经过的时间为 分钟。
所以正确答案是 B。
The two observations lie on opposite sides of the instant when the hands coincide. Their signed angular separation changes by Since the minute hand gains on the hour hand at per minute, the elapsed time is minutes.
Thus, the correct answer is B.