六年级奥数试题及答案:钟面问题
王师傅2点多钟开始工作时,时针与分针正好重合在一起.5点多钟完工时,时针与分针正好又重合在一起.王师傅工作了多长时间?点击下一页查看答案
考点:时间与钟面.
分析:从夜里0:00开始分针和时针同时出发,一周的路程为360度,分针速度为360度÷60分,时针的速度为30度÷60分,分钟快,时针慢,分针跑一周后继续跑追上时针,两者间距为360度,时间假设为t分钟,列式计算:(360度÷60分)×t分-(30度÷60分)×t分=360度,
http://www.aoshu.com/e/20140228/data:image/png;base64,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
解答:从夜里0:00开始分针和时针同时出发,一周的路程为360度,分针速度为360度÷60分,时针的速度为30度÷60分,分钟快,时针慢,分针跑一周后继续跑追上时针,两者间距为360度,时间假设为t分钟,列式计算:
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点评:判断出2点重合和5点的重合分别是第二次重合和第五次重合,根据时针和分针的运动规律,分钟运动的时间即表从0:00开始的总时间,由分化成小时减去60的倍数即得现在的时间是几时几分.
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