Understanding Clock Hand Movements
To determine the fraction of a clockwise revolution made by the hour hand of a clock during the specified intervals, we need to analyze each segment carefully.
1. First Segment: 22 to 5
- The hour hand moves from 10 (22 hours) to 5.
- This is a movement of 7 hours (10 to 11, 11 to 12, 12 to 1, 1 to 2, 2 to 3, 3 to 4, 4 to 5).
- Fraction of the revolution: 7/12 (since the full circle is 12 hours).
2. Second Segment: 4 to 10
- The hour hand moves from 4 to 10.
- This is a movement of 6 hours (4 to 5, 5 to 6, 6 to 7, 7 to 8, 8 to 9, 9 to 10).
- Fraction of the revolution: 6/12 = 1/2.
3. Third Segment: 5 to 2
- The hour hand moves from 5 to 2.
- This is a movement of 9 hours (5 to 6, 6 to 7, 7 to 8, 8 to 9, 9 to 10, 10 to 11, 11 to 12, 12 to 1, 1 to 2).
- Fraction of the revolution: 9/12 = 3/4.
4. Fourth Segment: 7 to 7
- The hour hand moves from 7 to 7, completing a full cycle.
- This is a movement of 12 hours (7 to 8, 8 to 9, 9 to 10, 10 to 11, 11 to 12, 12 to 1, 1 to 2, 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 7).
- Fraction of the revolution: 12/12 = 1.
Total Movement Calculation
- First Segment: 7/12
- Second Segment: 1/2 = 6/12
- Third Segment: 3/4 = 9/12
- Fourth Segment: 1 = 12/12
Final Total
- Total movement = (7/12) + (6/12) + (9/12) + (12/12) = 34/12 = 2.83 revolutions.
Fraction of a Clockwise Revolution
- The total movement in terms of a single revolution is 2.83 revolutions or 34/12.
Thus, the hour hand of the clock turns through a total fraction of 34/12 in a clockwise direction during the specified movements.