7.5 hours
Hour Hand Movement Calculation
The hour hand on an analog clock completes a full 360-degree rotation in 12 hours.
This means its speed is:
$ \text{Speed} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} $
Worker's Stay Duration Calculation
The worker observed the hour hand moved 225 degrees.
To find the time duration (how long she stayed), divide the total angle moved by the hour hand's speed:
$ \text{Time} = \frac{\text{Angle Moved}}{\text{Speed}} $
Plugging in the values:
$ \text{Time} = \frac{225 \text{ degrees}}{30 \text{ degrees/hour}} $
$ \text{Time} = 7.5 \text{ hours} $
The worker stayed in the factory for 7.5 hours.
Important Questions from Clocks
- Rohit goes to a restaurant for lunch at about $1 \text{ PM}$. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?
- On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
- In a 12-hour clock that runs correctly, how many times do the second, minute,and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a dayto 3 AM the next day?
- It is quarter past three in your watch. The angle between the hour hand and the minute hand is ______
- The minute-hand and second-hand of a clock cross each other __________ times between 09:15:00 AM and 09:45:00 AM on a day.
