Clock Hands at 3:15

Question

What is the angle between the hour and minute hands of an analog clock at 3:15?

Accepted Answer

At 3:15 the minute hand points exactly at the 3, that is 90° from 12. The hour hand is not at the 3: it drifts 30° per hour = 0.5° per minute. Fifteen minutes past three, it has moved 3 times 30° + 15 times 0.5° = 90° + 7.5° = 97.5°. Angle between the hands: 97.5° - 90° = mathbf7.5°. The general formula (worth memorizing for speed rounds): at H:M the angle is left|30H - 5.5Mright| (take the value or 360 minus it, whichever le 180). The trap answer "0°" forgets the hour hand moves continuously, exactly the kind of hidden drift assumption these firms enjoy testing.

Clock Hands at 3:15

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