82. Andrey and Grandpa Grisha went mushroom picking sometime between six and seven in the morning, at the moment when the clock hands were aligned. They returned home between twelve and one in the afternoon, at the moment when the clock hands were pointing in exactly opposite directions. How long did their mushroom "hunt" last?
82. In 1 hour, the minute hand makes a full revolution (its end describes a circle), while the hour hand travels $\frac{1}{12}$ of the circumference. Therefore, in one hour, the minute hand will travel more than the hour hand by $\frac{11}{12}$ of the circumference. By the time the minute hand travels from 12 to 6, i.e., $\frac{1}{2}$ of the circumference, the hour hand will travel $\frac{1}{24}$ of the circumference, i.e., at 6:30, the minute hand will lag behind the hour hand by $\frac{1}{24}$ of the circumference. It will catch up with the hour hand in $\frac{1}{22}$ of an hour $\left(\frac{1}{24} : \frac{11}{12} = \frac{1}{22}\right)$. The clock will show $6 \frac{6}{11}$ hours $\left(6 \frac{1}{2} + \frac{1}{22} = 6 \frac{6}{11}\right)$. Similar reasoning leads to the conclusion that when the hour hand is between 12 and 1, and the minute hand is directly opposite to it, the clock will show $12 \frac{6}{11}$ hours. Therefore, the mushroom "hunt" lasted 6 hours $\left(12 \frac{6}{11} - 6 \frac{6}{11} = 6\right)$.