Question

How many times the minute hand of a clock overlaps with the hour hand from 9:00 am to 4:00 pm in a day?

Answer 1

it's 6 times the minute hand overlaps hour hands i.e.(10,11,12,1,2,3)
any doubts can ask me

Answer 2

Check How many times a day do a clock’s hands overlap

• If that doesn’t explain well, check the below math I did to solve it :

• 1 day = 24 hours.

• Minute hand:-

• In 60 minutes covers 360 degree, so speed of minute hand is 6 degree per minute.

• Hour hand:-

• In 12 hours covers 360 degree, so speed of hour hand is 30 degree per hour or 1/2 degree per minute.

• Angular relative speed between minute and hour hand = 6–1/2 = 11/2 degree per minute.

•¤Let’s see when do minute hand and hour hand overlap, basically start with a reference of 12:00 AM, At this point both are at same position but will now move at different speed.

• They will overlap at the point when the relative speed between them covers the angular distance of 360 degree.

• So, time = angular distance/angular relative speed = 360/ (11/2) = 720/11 minutes.

• In every 720/11 minute, the two hands overlap.

• So, the number of times the two hands overlap will be equal to number of such minutes in 24 hour duration (24*60 minutes). i.e equal to 24 *60/ (720/11) which is

24 * 60 * 11/720 = 22 times.

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