*23/12/2021*

In primary schools, students sometimes are asked to find the time when the hour and minute hands of a clock overlap. For example, after 1 p.m., when will the hands overlap? Our impression tells it is about 1:05 p.m. But can we find the exact time? Below is the solution.

At 1 p.m., the two hands form an angle of 30 degree.

Let the time be t minute after 1 p.m. Then

since the minute hand turns 6 degree/min whereas the hour hand turns 0.5 degree/min

therefore 6t=0.5t+30

t=60/11=5 5/11

So, the required time is exactly at 1: 5 5/11 p.m., consistent with our impression.

Can we find when the hands next overlap or when the hands form a right angle, a straight line or any angle? Is there a general formula?

Click the following link if you want to know more.

https://drive.google.com/file/d/13W6zpmiUJPrx3vAYdc7s5E4DzMHyng2_/view?usp=sharing

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