When do the hour hand and the minute hand overlap on the clock?

It is never late to understand the simple calculation and you will steal the limelight at any party because you are cleverer than others.

When you know how to work out the accurate time when the hour hand and the minute hand overlap, it is easy for you to figure out:

When will the two hands be in a straight line?

When will the two hands form right angles in an hour time?

First of all, you have to know that the minute hand runs faster than the hour hand. The velocity of the former is greater than that of the latter. When the second hand has run 60 minutes, the hour hand has just finished one twelfth of a clock. Hence the time to catch up with the hour hand is as follows:

Time = 5 divided by (60-5) = 1/11

When 1/11 is multiplied by 60 minutes, we get 5 and 5/11 minutes.

It means that the two hands overlap at 01: 05: 5/11 a.m. or p.m. after twelve o’ clock.

When it is at noon or midnight, they overlap for sure.

Accordingly,

When it is two o’ clock,

2/11 is multiplied by 60 minutes and we get 10.9090 minutes. It means that they overlap at 02: 10: 54 am/pm. (0.9090 x 60 seconds = 54 seconds)

Note: The denominator is constant and it must be 11. As for the numerator, it depends on what o’ clock is. For example, if it is 7 o’ clock, the fraction is 7/11.

I have an appointment with you when the hands overlap after 9 o’ clock next morning. Could you tell me the exact time, please? Remember not to be late!