1962 AHSME Problems/Problem 35
Problem
A man on his way to dinner short after p.m. observes that the hands of his watch form an angle of
. Returning before
p.m. he notices that again the hands of his watch form an angle of
. The number of minutes that he has been away is:
Solution
Let be the number of minutes after 6:00. Let
be the angle, in degrees, of the hour hand (with
at the top and increasing in the clockwise direction); similarly, let
be the angle of the minute hand. We want
. This is equivalent to
The difference between the two values of
is
.