时钟的分针和时针将在上午6点至上午7点之间的某个时间最接近60 o
(A)上午6:22
(B)上午6:27
(C)上午6:38
(D)上午6:45答案: (A)
解释:
Speed of the Hour hand = ( 360 degree ) / ( 12 * 60 minutes )
= 0.5 degree / minute.
Speed of the minute hand = ( 360 degree ) / ( 60 minutes )
= 6 degree / minute.
凌晨6点,时针将垂直向下指向时钟6,而分针将垂直向上指向时钟12。 (因此它们是相对的,它们之间有180度的间隙)。
现在,t分钟后,这两只手之间的夹角将是以下两只手之一:
(180 - 6t) + 0.5t, when the minute hand is
behind the hour hand or,
6t - (180 + 0.5t), when the minute hand is
ahead of hour hand,
Now the the question asks for angle of 60 degree.
Hence,
(180 - 6t) + 0.5t = 60 , we get t = 21.8 minute
and
6t - ( 180 + 0.5t ) = 60, we get t = 48 minutess
因此,最接近答案的时间是22分钟,即上午6.22。因此答案是A。这个问题的测验