# Are u good in math?

1. Jan 24, 2005

### sheperd

Hi

I just want to know in a clock, 12’O clock both needles (hour and minute) will coincide (one over the other)
My question is exactly at what time both needles will coincide again after 12’o clock

Good luck.

2. Jan 24, 2005

### Kahsi

13.05 :shy: ?

3. Jan 24, 2005

### allen74delval

movement of hourhand:
hour hand moves 360 degree in 12 hours.
one hour is 30 degree. or 60 minutes =30 degree movement
6 minutes = 3 degrees
one minute= .5 degrees.
5 minutes =2.5 degrees

minute hand moves 360 degrees in 60 minutes
5 minutes = 30 degrees
one minute =6 degrees
at 1:05 the hour hand is at 32.5 degrees . minute hand is at 30 degrees

4. Jan 24, 2005

### krab

Let $\theta_h$ be the angle of the hour hand away from the 12, and $\theta_m$ be the angle of the minute hand away from the 12. Then I think you can see that
$$12\,\theta_h=\theta_m+360^\circ n$$
where n is an integer. Now set $\theta_m=\theta_h$ and solve for each n. For example, the first coincidence is at $\theta_{h,m}=360^\circ/11$, or 1:05:27.2727...

5. Jan 25, 2005

### Tide

Yes, but can you do it with hour, minute and second hands all coinciding? :-)

6. Jan 25, 2005

12:00