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AMIT AHLAWAT

· started a discussion

· 1 Months ago

explain the formula (Question: 195615.0 )

explain

Question:
At what time between 3 pm and 4 pm will both the hands of a clock overlap each other?
Options:
A) 4 minutes past 3 
B) 30 minutes past 3 
C) 16\(\cfrac{4}{11}\) minutes past 3 
D) None of these
Solution:
Ans: (c) 


Knowledge Expert

· commented

· 1 Months ago

Dear Student,

I have formula for clocks coincide:
= (5(H)+0)*(12/11) where H = 3.


One more comprehensive solution:

Let x be the number of minutes after 3:00 that the hour and minute hands overlap.
Since the hour hand moves 360∘ over a 24-hour period,
so it moves 360∘/(12×60)=0.5∘ per minute. The hour hand would be at 90∘ at time 3:00, therefore, it would be at 90∘+0.5∘×x at the time that the hands overlap.
For the minute hand: it moves 360∘ every hour, so it moves 360∘/60=6∘ every minute. And since it starts at an angle of 0∘ at 3:00, the minute hand should be at the angle of 6∘×x when they overlap.
Now, set them equal to each other, you get:
90+0.5x = 6x
180+x=12x
180=11x
x=180/11
∴The hour and minute hands overlap each other 180/11 minutes after 3:00.

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