A number theory problem by sudoku subbu
Number Theory
Level
2
BETWEEN 12 : 00 AND 13 : 00 THERE ARE 2 TIMES WHEN THE HANDS ON A CLOCK ARE EXACTLY AT RIGHT ANGLES . HOW MANY MINUTES APART ARE THESE TWO TIMES
The answer is 32.727273.
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1 solution
Calculate the rate(speed) which the angle changes (also known as the angular velocity) for both the hour hand and minute hand. The unit is degrees per second.
Minute hand: 360 degrees / 60 minutes = 6
The hour hand only moves 30 degrees in an hour. (The angle between 1200 and 1300)
Hour hand: 30 degrees / 60 minutes = 0.5
The difference in angle between the two hands can be calculated as below:
(minute)(6) - (minute)(0.5)
By equating that formula to 90 degrees and 270 degrees (which is 360-90), we can calculate the exact minutes when the hands of the clock are at right angles.
(minute A)(6) - (minute A)(0.5) = 90
Minute A = 180/11
(minute B)(6) - (minute B)(0.5)
Minute B = 540/11
Finally,
Minute B - Minute A = 32.727 minutes apart