A clock has Hour and Minute hands of the same length and NO NUMERALS on its face.

At what time between 6 O'clock and 7 O'clock will the time on the clock appear to be the same when the reflection of the clock is read on a mirror?

Source: Lewis Carroll

If t is minutes past time=0, and we start at 6:00, the H and M functions of t are in degrees clockwise from vertical.
H(0) = 180
M(0) = 0

H(t) = 180(degrees) + (1/2)(degrees/min) * t(min)
M(t) = 6t

At time t, each hand will be equal degrees from the 180 position:
Hour hand: t/2
Min hand:  180 - 6t

t/2 = 180 - 6t -->  t = 360/13
  t = 27.692307692307693 minutes after the hour

For time format HH:MM:SS
Time:  06:27:41 plus .538461538461576 seconds

Posted by Larry on 2023-09-10 15:46:15