36.52 A person looked at their watch just after 6:00 PM while having dinner, and the hands formed a $110^{\circ}$ angle. They returned before 7:00 PM and noticed the hands also formed a $110^{\circ}$ angle. The total minutes spent dining by this person is
(A) $36 \frac{2}{3}$.
(B) 40 .
(C) 42 .
(D) 42.4 .
(E) 45 .
(13th American High School Mathematics Examination, 1962)
[Solution] Let $x$ be the angle the hour hand has moved through during this period, then the angle the minute hand has moved through is $12x$.

From the diagram, the angle moved by the minute hand is also $220 + x$, so $220 + x = 12x$, giving $x = 20$.
During this time, the minute hand has moved through $12x = 240$ degrees, and since the minute hand moves $6^{\circ}$ per minute, the time taken by the minute hand is
$$
\frac{240}{6} = 40 \text{ (min). }
$$

Therefore, the answer is $(B)$.