Understanding Clock Hand Movement

To determine how long the worker stayed at the factory, we need to understand how the hour hand of a clock moves. A standard clock face is a circle, which measures 360 degrees.

• The hour hand completes a full circle (360 degrees) in 12 hours.
• This means that in 1 hour, the hour hand moves a certain number of degrees.

We can calculate the speed of the hour hand in degrees per hour:

Speed of hour hand = $\frac{360 \text{ degrees}}{12 \text{ hours}}$

Speed of hour hand = $30 \text{ degrees per hour}$

Calculating Time Duration

The worker noticed that the hour hand moved by 225 degrees. We know the speed of the hour hand is 30 degrees per hour. To find out how long she stayed, we divide the total degrees moved by the speed of the hour hand.

Duration of stay = $\frac{\text{Total degrees moved by hour hand}}{\text{Speed of hour hand}}$

Duration of stay = $\frac{225 \text{ degrees}}{30 \text{ degrees per hour}}$

Let's perform the division:

Duration of stay = $7.5 \text{ hours}$

Final Time Spent

The calculation shows that the worker stayed for 7.5 hours. This can also be expressed as 7 hours and 30 minutes, as 0.5 hours is half of an hour, which is 30 minutes.

Therefore, if the hour hand moved by 225 degrees, the worker's stay at the factory was 7.5 hours.