Problem 3 · 2012 Math Kangaroo
Easy
Geometry & Measurement
clock-calendar
A wristwatch lies on the table with its face upwards. The minute hand points towards north-east. How many minutes have to pass for the minute hand to point towards north-west for the first time?
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Answer: A — 45
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Hint 1 of 2
A minute hand sweeps the whole clock face in 60 minutes.
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Hint 2 of 2
Going clockwise, how much of a full turn takes you from north-east round to north-west?
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Approach: fraction of a full turn
- The minute hand turns clockwise, a full circle (360°) in 60 minutes.
- From north-east, turning clockwise, it reaches south, then west, then north-west: that is 270° of the turn.
- 270° is three-quarters of 360°, so it takes three-quarters of 60 minutes = 45 minutes.
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