how often does the minute hand pass the hour hand on an analog clock?

how often does the minute hand pass the hour hand on an analog clock?


As the hour hand must move a bit more than one hour to catch up to the minute hand. Specifically it moves 12/11 of an hour or 65.454545 minutes. Thus the correct times where minute hand pass the hour hand are:

0:00:00 (midnight)
1:05:27
2:10:55
3:16:22
4:21:49
5:27:16
6:32:44
7:38:11
8:43:38
9:49:05
10:54:33
12:00:00 (noon)
13:05:27
14:10:55
15:16:22
16:21:49
17:27:16
18:32:44
19:38:11
20:43:38
21:49:05
22:54:33
24:00:00 (which doesn’t count because it’s in the next day)
So there are 22 crossings. Note that there is NO overlap in the expected area of 11:55 because it happens at 12:00. You can spin the time setting knob on an analog clock and see this easily.
No. of hours in a day = 24 hours
No .of passing between minute hand and hour hand = 22
Time needed by minute hand to pass the hour hand = 24 hours/22 = 1 hours 1/11 minute.

What is the angle between the minute hand and the hour hand at 3:15 on an analog clock?

Question: What is the angle between the minute hand and the hour hand at 3:15 on an analog clock?

Answer:
Every 12 hours hours hand runs 360 deg. So for every hour it makes 260/12=30 deg.

Since its 15 mins., which is 1/4 hour, the hour hand should move 30*1/4 deg=7.5 deg from 3.

So the Angle between minutes hand and hours hand is 7.5 Deg