1 |
12 |
设从0时开始,过z分钟后分针与时针成60°的角,此时分针比时针多走了n圈(n=0,1,2,…,11),则x-
x |
12 |
x |
12 |
解得x=
120 |
11 |
120 |
11 |
分别令n=0,1,2,3,…,11,即得本题的所有解(精确到秒),共22个:
0:10:55 1:16:22 2:21:49 3:27:16 4:32:44 5:38:11
6:43:38 7:49:05 8:54:33 10:00:00 11:05:27
0:54:33 2:00:00 3:05:27 4:10:55 5:16:22 6:21:49
7:27:16 8:32:44 9:38:11 10:43:38 11:49:05
答:在0时到12时之间,钟面上的时针与分针成60度角共有 22次.
故答案为:22.