How many times a day do the minute and hour hands of a clock overlap?


Updated: Nov. 28, 2020 — Training Time: 2 minutes
Overseen by: Archangel Macsika

Topic: Data Science.

Difficulty: Advanced.

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Objective: How many times a day do the minute and hour hands of a clock overlap?

Short Answer: 22 times.

Full Solution

This will require you to flex your arithmetic skills and knowledge of speed, distance and time.

From physics, you know that time = distance/speed.
There's 1440 minutes in a day.

The minute hand of the clock moves 360 degrees in 60 minutes. So, the speed of a minute hand in 1 minute is:
360 / 60 = 6 degrees per minute.

The hour hand of clock moves 360 degrees in 12 hours (720 minutes). So, the speed of an hour hand is:
360/720 = 0.5 degrees per minute.

Based on the concept of relative speed, when two objects say, A & B move in the same direction, then their relative speed is A - B.
Therefore, speed between minute and hour hand is:
6 – 0.5 = 5.5 degrees per minute.

If we consider 12 am as the reference point where minutes and hours coincide, the distance covered between them is 360 degrees.

Now, time = distance/speed, which is 360/5.5 = 65.45 minutes.

This means that every 65.45 minutes, the minute hand and hour hand meets.

Therefore, in a day which is 1440 minutes, the minute hand and hour hand meets:
1440/65.45 = 22

So, the minute hand and hour hand meets 22 times in a day.

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