A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?
- A3.75 hours
- B4 hours and 15 mins
- C8.5 hours
- D7.5 hours
Solution & Step-by-step Explanation
Understanding Hour Hand Movement on a Clock
This problem involves calculating the time duration a worker stayed at a factory based on the movement of the hour hand on a clock. We need to understand how the hour hand moves and relate its movement in degrees to the time elapsed.
Clock Basics and Hour Hand Speed
- A clock face represents a full circle, which is 360 degrees.
- The hour hand completes a full circle (360 degrees) in 12 hours.
- To find the speed of the hour hand in degrees per hour, we divide the total degrees by the total hours: Speed = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour}
- This means the hour hand moves 30 degrees every hour.
Calculating the Time Duration
We are given that the hour hand moved 225 degrees. We can use the speed calculated above to find out how much time this movement corresponds to.
Step-by-Step Calculation
1. Identify the total degrees moved: The problem states the hour hand moved 225 degrees.
2. Recall the hour hand's speed: We calculated that the hour hand moves at a speed of 30 degrees per hour.
3. Calculate the time elapsed: The time duration can be found by dividing the total degrees moved by the speed of the hour hand. Time = \frac{\text{Total Degrees Moved}}{\text{Speed of Hour Hand (degrees per hour)}} Time = \frac{225 \text{ degrees}}{30 \text{ degrees/hour}}
4. Perform the division: Time = \frac{225}{30} \text{ hours} Time = \frac{22.5}{3} \text{ hours} Time = 7.5 \text{ hours}
5. Convert the decimal part to minutes (optional but helpful for clarity): The time is 7 full hours plus 0.5 hours. To convert 0.5 hours to minutes, multiply by 60: 0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}
6. State the final duration: The total time the worker stayed at the factory is 7 hours and 30 minutes.
Final Answer Verification
The calculation shows that a movement of 225 degrees for the hour hand corresponds to 7.5 hours. This value aligns with one of the options provided.
This problem involves calculating the time duration a worker stayed at a factory based on the movement of the hour hand on a clock. We need to understand how the hour hand moves and relate its movement in degrees to the time elapsed.
Clock Basics and Hour Hand Speed
- A clock face represents a full circle, which is 360 degrees.
- The hour hand completes a full circle (360 degrees) in 12 hours.
- To find the speed of the hour hand in degrees per hour, we divide the total degrees by the total hours: Speed = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour}
- This means the hour hand moves 30 degrees every hour.
Calculating the Time Duration
We are given that the hour hand moved 225 degrees. We can use the speed calculated above to find out how much time this movement corresponds to.
Step-by-Step Calculation
1. Identify the total degrees moved: The problem states the hour hand moved 225 degrees.
2. Recall the hour hand's speed: We calculated that the hour hand moves at a speed of 30 degrees per hour.
3. Calculate the time elapsed: The time duration can be found by dividing the total degrees moved by the speed of the hour hand. Time = \frac{\text{Total Degrees Moved}}{\text{Speed of Hour Hand (degrees per hour)}} Time = \frac{225 \text{ degrees}}{30 \text{ degrees/hour}}
4. Perform the division: Time = \frac{225}{30} \text{ hours} Time = \frac{22.5}{3} \text{ hours} Time = 7.5 \text{ hours}
5. Convert the decimal part to minutes (optional but helpful for clarity): The time is 7 full hours plus 0.5 hours. To convert 0.5 hours to minutes, multiply by 60: 0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}
6. State the final duration: The total time the worker stayed at the factory is 7 hours and 30 minutes.
Final Answer Verification
The calculation shows that a movement of 225 degrees for the hour hand corresponds to 7.5 hours. This value aligns with one of the options provided.