1962 AHSME Problems/Problem 35
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:
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 .