Starting at 8am determine the # of times in 24hrs for which the hour & min hands on the clock coincide?

Question

Starting at 8am determine the # of times in 24hrs for which the hour & min hands on the clock coincide?

Answer 1

In any 12 hours, the hour and minute hands coincide 11 times.  You might think it would be 12 times, but it's really 11.

Since the hour hand also completes one revolution during this time, it cuts the number of times the minute hand passes it down from 12 to 11.

Starting at 8 am, they would coincide at:

1. 8:42 or so

2. 9:47 or so

3. 10:52 or so

4. 12 noon

5. 1:05

6. 2:10

7. 3:15

8: 4:22 or so

9. 5:27

10: 6:33 or so

11. 7:38

11 times in 12 hours - So, in the course of 24 hours, they would coincide 22 times.

Answer 2

On a 24-hr clock, the hr hand goes around once, and the minute hand goes around 24 times, and coinciding once each hour.

On a 12-hr clock, the hr hand goes around twice. The minute hand still goes around 24 times, and still coincides with the hr hand 24 times.

On a digital clock, there are no hands.

Answer 3

23

Answer 4

Why would I want to waste my time doing that for?  What drugs are you on?