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?

The correct option is 7.5 hours.

To find the duration of the worker's stay at the factory, we can calculate how many degrees the hour hand of a clock moves per hour.

A standard clock face is a circle containing 360° and is divided into 12 equal hours. The hour hand completes one full rotation of 360° in 12 hours.

First, we find the angular speed of the hour hand per hour:

$$\text{Angular speed}=\frac{360°}{12\text{ hours}}=30°\text{ per hour}$$

This tells us that the hour hand moves by 30° for every hour that passes.

Next, we are given that the hour hand moved by 225° during the worker's stay. To find the duration of her stay, we divide the total angle of movement by the angular speed of the hour hand:

$$\text{Duration of stay}=\frac{225°}{30°\text{/hour}}$$

Calculating the value:

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

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