1962 AMC 12 Problem 35

Question

A man on his way to dinner shortly after

6{:}00

p.m. observes that the hands of his watch form an angle of

110^\circ.

Returning before

7{:}00

p.m. he notices that again the hands of his watch form an angle of

110^\circ.

The number of minutes that he has been away is:

36\dfrac23

40

42

42.4

45

During the interval, the minute hand gains on the hour hand at

5.5^\circ

per minute

Between the two observations, the signed separation changes from

110^\circ

to

-110^\circ

The two observations lie on opposite sides of the instant when the hands coincide. Their signed angular separation changes by

220^\circ.

Since the minute hand gains on the hour hand at

6-0.5=5.5^\circ

per minute, the elapsed time is

\frac{220}{5.5}=40

minutes.

Thus, the correct answer is B.

Problem 35 in other years