The Right Time
Geometry
Level
2
During each hour, the clock hands will always make a right angle twice as shown above.
Will the time gap between these 2 instances be constant for every hour?
No
Yes
Not enough information
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1 solution
The minute hand will move 6 3 6 0 = 6 degrees clockwise every minute while the hour hand will move 6 0 3 0 = 0 . 5 degree, for each hour only accounts for 1 2 3 6 0 = 3 0 degrees. Thus, each minute the angle between these hands will decrease by 6 − 0 . 5 = 5 . 5 degrees.
Once the hands make the first right angle, they will continue to move closer to each other until they are superimposed (making 0 degrees) and will start to form increasing angle of constant rate to eventually make a second right angle.
In other words, the time gap between these right angles equal 5 . 5 9 0 + 9 0 = 1 1 3 6 0 ≈ 3 3 minutes for every hour.