A clock hangs on the wall of a railway station, 71 ft. 9 in. long and 10 ft. 4 in. high. Those are the dimensions of the wall, not of the clock! While waiting for a train we noticed that the hands of the clock were pointing in opposite directions, and were parallel to one of the diagonals of the wall. What was the exact time?

• Let us determine a diagonal of the wall
  
  10 ft 4 inches = 124 inches
  and
  71 ft 9 inches = 861 inches
  
  the tangent of the angle between the
  bottom and top and a diagonal is
  
  124/861
  
  the inverse tangent of this is 8.1953°
  
  thus the hour hand would have to be
  at an angle of 81. 80469° to the
  right of 12 o' clock high if the time is
  ANY where between 12 and 3 in order
  for this premise to be true.
  
  At 3:00 it is at 90° and at 12:00 it is at zero.
  
  The hour hand reaches this parallel position at
  
  81.80469357
  ▬▬▬▬▬▬ X 3 hours
  ...90
  
  which is
  
  2.726823119 hours after 12
  
  or
  
  43.60938714 minutes after 2:00
  
  or 2:43:36
  
  I just verified that the minute hand would be at an angle of
  
  261.6563228° at that time which is
  81.65° away from the 6:00 position so it would, appear directly
  opposite and within that minute, should be directly opposite the hour
  hand.
  
  Although that could round to 2:44, the exact time HAS not reached 2:44 yet
  during the 2:43 minute. Therefore, the answer has to be
  
  d which is 2:43
• 11 years agoHelpfull: Yes(5) No(3)
• there are four possiblities
  11:25
  5:55
  7:35
  1:35
• 11 years agoHelpfull: Yes(0) No(1)