$36 \cdot 54$ A person starts a journey when the two hands of the clock coincide between 8 and 9 in the morning, and arrives when the two hands of the clock are exactly $180^{\circ}$ apart between 2 and 3 in the afternoon. Therefore, the journey took
(A) 6 hours.
(B) 6 hours $43 \frac{7}{11}$ minutes.
(C) 5 hours $16 \frac{4}{11}$ minutes.
(D) 6 hours 30 minutes.
(E) None of the above.
(6th American High School Mathematics Examination, 1955)
[Solution] Let the hour and minute hands coincide at 8 o'clock and $x$ minutes. Since at 8 o'clock, the minute hand is 40 units behind the hour hand (considering a full circle as 60 units), when they coincide (the minute hand catches up with the hour hand):
$$
x-\frac{x}{12}=40 \text {, we get } x=43 \frac{7}{11} \text { (minutes). }
$$

Similarly, between 2 o'clock and 3 o'clock, the hour and minute hands form a $180^{\circ}$ angle at 2 o'clock and $43 \frac{7}{11}$ minutes.
In summary, this person spends a total of 6 hours.
Therefore, the answer is $(A)$.