11. (5 points) Xiao Hong left home close to 11 AM, at which time the hour and minute hands of the clock overlapped. She returned home close to 5 PM the same day, at which time the hour and minute hands of the clock were in opposite directions (in a straight line). How many hours did Xiao Hong stay out?
【Answer】Solution: The minute hand moves $\frac{360^{\circ}}{12}=30^{\circ}$ per hour.
When Xiao Hong leaves, the minute hand and the hour hand are $360^{\circ}-30^{\circ} \times 2 \times 60^{\circ}=300^{\circ}$ apart.
When she returns, the minute hand and the hour hand are $30^{\circ} \times 4=120^{\circ}$ apart.
The minute hand has also surpassed the hour hand by $30^{\circ} \times 4=120^{\circ}$.
It has surpassed the hour hand by another $180^{\circ}$.
Throughout the process, the minute hand has moved $120^{\circ}+180^{\circ}=300^{\circ}$ more than the hour hand. Therefore, when Xiao Hong leaves and returns, the position of the minute hand has not changed; only the hours are added, which is 10 o'clock - 4 o'clock $=6$ hours.

The answer is: 6.