At What Time Do Hour and Minute Needles Coincide After 12'O Clock?

[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.

 

[Kahsi]

13.05 :shy: ?

 

[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

 

[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...

 

[Tide]

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

 

[vincentchan]

12:00
this is the only answer...

 

[Tide]

Can you prove it? :-)