Lee's Math Tuition

Lee's Math Tuition

for DSE Math CP and M2
over 40 years of teaching experience
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Mød Google Drev – ét sted til alle dine filer 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.

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