Clock Hands Angle at 3:15: The Solution
Interview logic question on calculating angles with clock hands
The riddle
What angle do the hands of a clock form at 3:15? The clock face has 12 hours and 360 degrees, and the minute hand indicates the minutes.
Need a hint?
Calculate where the hour hand is at exactly 3:00, then how far it has moved during the following 15 minutes.
Show the answer and the solution
Answer: 7.5 degrees: the minute hand is on the 3 (90 degrees) and the hour hand is at 97.5 degrees, a gap of 7.5 degrees.
The reasoning
At 3:15, the minute hand has moved for a quarter of an hour: it points to the 3, 90 degrees from the 12, since each minute is worth 6 degrees. The hour hand covers 360 degrees in 12 hours, that is 0.5 degrees per minute. At exactly 3:00 it was at 90 degrees, and during the following 15 minutes it moves 15 × 0.5 = 7.5 degrees, reaching 97.5 degrees. The gap between the two hands is therefore 97.5 minus 90 = 7.5 degrees.
What next?
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