FILE No.57Unsolved
An analog wall clock lay on the study floor. Its hands had stopped at 3:15.
The detective is trying to use "the angle between the hands" as a clue to what happened when the clock fell.
Angles are measured clockwise from the 12 o’clock position. In one hour the hour hand moves 30 degrees and the minute hand moves 360 degrees.
At 3:15, what is the smaller angle between the hour hand and the minute hand?
If you get stuck, open the hints one at a time, in order.
At what angle is the minute hand after 15 minutes?
At what angle is the hour hand at exactly 3:00, and how much further does it move in 15 minutes?
The difference between the two positions is the angle.
At 3:15, what is the smaller angle between the hour hand and the minute hand?
Choose the answer closest to the truth.
7.5 degrees
The answer is 7.5 degrees.
In 15 minutes the minute hand has moved 90 degrees from the 12 position (it is at the 3 on the dial). The hour hand would be at 90 degrees at exactly 3:00, but it keeps moving during the 15 minutes: 30 degrees x (15 / 60) = 7.5 degrees. The hour hand is at 90 + 7.5 = 97.5 degrees.
The minute hand is at 90 degrees and the hour hand at 97.5 degrees. The difference is 7.5 degrees. If you assume the hour hand is on the 3, you wrongly get 0 degrees.
You assume that at 3:15 both the hour and the minute hand are on the 3 and overlap.
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