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:

$36\dfrac23$

$40$

$42$

$42.4$

$45$

Answer: B

Concepts:clock relative speed

Difficulty rating: 1570

Small Hint:

During the interval, the minute hand gains on the hour hand at $5.5^\circ$ per minute

Big Hint:

Between the two observations, the signed separation changes from $110^\circ$ to $-110^\circ$

Solution:

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.

1962 AMC 12 Problem 35

Answer: B

Difficulty rating: 1570

Small Hint:

Big Hint:

Solution:

Problem 35 in Other Years