Minutes hand: The larger hand in the clock denotes the minute hand or long hand.
Seconds hand: The hand that indicates the seconds on a clock or watch.
Hours hand: The shorter hand in the clock denotes the hours hand.
Too fast and too slow:
Example 1:
At what time between 4 and 5, will the hands of a clock coincide?
Solution:
Example 2:
At what time between 10 and 11 will the minute and hour hand be at right angles?
Solution:
Considering that hour hand is at 10, to make a 90-degree angle with the hour hand, the minute hand has to be at 1 or 7.
For the first right angle, minute hand has to cover a relative distance of (1*30) = 30°.
For the 2nd right angle, minute hand has to cover a relative distance of (7*30)= 210°.
We know that the relative speed between the two hands is of \(5\frac{1}{2}°\) per minute.
Hence, time required for the \(1^{st}\) right angle = \(\frac{30 \times 2}{11}\) = \(\frac{60}{11}\) or \(5\frac{5}{11}\) minutes.
Time required for the \(2^{st}\) right angle = \(\frac{210 \times 2}{11}\) = \(\frac{420}{11}\) = \(38\frac{2}{11}\) minutes.
Example 1:
The angle between the minute hand and the hour hand of a clock when the time is 4:20 is:
Solution:
Example 2:
The angle between the minute hand and the hour hand of a clock when the time is 3:30 is:
Solution:
2. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25?
Solution:
3. A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on fourth day?
Solution:
4. Find at what time between 4 and 5 o’clock will the hands of a clock be at right angle?
Solution:
5. At what time between 2 and 3 o’clock will the hands of a clock be together?
Solution: