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?

To find out how long the worker stayed in the factory, we can determine the relationship between the movement of the hour hand in degrees and the elapsed time in hours.

Step 1: Determine the rate at which the hour hand moves.
A standard clock face is a full circle, which is equal to 360 degrees. The hour hand completes one full rotation of the clock face in 12 hours.

$\text{Angular speed of the hour hand}=\frac{360\text{degrees}}{12\text{hours}}=30\text{degrees per hour}$

Step 2: Calculate the duration of the stay.
The worker noticed that the hour hand moved by 225 degrees during her stay. We divide the total angle of movement by the hourly rate of the hour hand to find the total time spent at the factory:

$\text{Duration of stay}=\frac{225\text{degrees}}{30\text{degrees per hour}}=7.5\text{hours}$

Therefore, the worker stayed in the factory for 7.5 hours.