Directions
Concept of Clocks
- Type 1: Finding the time when the angle between the two hands is given.
- Type 2: Finding the angle between the 2 hands at a given time.
- Type 3: Questions on clocks gaining/losing time.
We will cover the first two types in this Lecture.
Important Points
- A clock is a complete circle having 360 degrees. It is divided into 12 equal parts i.e. each part is 360/12 = 30°.
- As the minute hand takes a complete round in one hour, it covers 360° in 60 minutes.
- In 1 minute it covers 360/60 = 6°/ minute.
- Also, as the hour hand covers just one part out of the given 12 parts in one hour. This implies it covers 30° in 60 minutes i.e. ½° per minute.
- This implies that the relative speed of the minute hand is 6 - ½ = 5 ½ degrees.
- We will use the concept of relative speed and relative distance while solving problems on clocks.
Some facts about clocks:
- Every hour, both the hands coincide once. In 12 hours, they will coincide 11 times. It happens due to only one such incident between 12 and 1'o clock.
- The hands are in the same straight line when they are coincident or opposite to each other.
- When the two hands are at a right angle, they are 15-minute spaces apart. In one hour, they will form two right angles and in 12 hours there are only 22 right angles. It happens due to right angles formed by the minute and hour hand at 3’o clock and 9'o clock.
- When the hands are in opposite directions, they are 30-minute spaces apart.
- If both the hour hand and minute hand move at their normal speeds, then both the hands meet after 65 5/11 minutes.