An analog clock's hour hand moves normally, but its minute hand reverses direction whenever it meets the hour hand. Initially, the clock reads 12:00 and both hands are moving clockwise.
Where will the minute hand be when the hour hand has completed a 12 hour circuit, and which direction will it be going?
When the minute hand is going prograde it takes the two hands 12/11 of an hour from meeting to meeting. When it's going retrograde, it takes 12/13 of an hour.
A pair of these takes 288/143 of an hour. In 12 hours that's 143/24 =~ 5.95833333333333 times this pairing, so it should be in the second portion (retrograde portion) of the pair of motions.
That's (6  143/24) of the 288/143 hours for the full cycle or 12/143 of an hour, which is 12/143 / (12/13) of the retrograde portion of the cycle or 1/11 of that retrograde period. 1/11 of the backward motion, taken of is 360/11 degrees clockwise from the 12 o'clock position or just over 32.7 degrees, or a little past the 1 o'clock position, headed toward the 1 and 12 o'clock positions, as it's retrograding.

Posted by Charlie
on 20230919 08:27:49 