Analog clock question?

Question

You know how at 12:00:00 the minute hand passes the hour hand? Well on a clock with no second hand when does the minute hand pass the hour hand? I mean 1:??:?? and 2:??:?? etc?

And please don't give me "1:05" and "2:10" because that's not the right answer.

Answer 1

How tricky do we want to get here?

The minute hand goes all the way around the clock face 12 times in 12 hours.

The hour hand goes all the way around the clock face 1 time in 12 hours.

So, if they start together, the minute hand will pass the hour hand 11 times in 12 hours, then exactly catch it at the end of 12 hours.

Since both hands move at a constant speed, we can just divide the clock face into 11ths

One eleventh of an hour is 5 minutes and 27 seconds (rounded to the nearest whole second)

So, the hands pass at:

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