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The Railway Station Clock (Posted on 2023-05-12) Difficulty: 2 of 5
A clock hangs on the wall of Lamsdale Railway Station. The wall is 71 ft. 9 in. long and 10 ft. 4 in. in height.

While waiting for the train, Ray and Sid noticed that the hands of the clock were pointing in the opposite directions and were parallel to one of the diagonals of the wall.

Determine the precise time.

**** Adapted from an original problem by H. E. Dudeney.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution close enough Comment 1 of 1
The wall is 71*12+9 = 861 inches long and 124 inches high.

The angles of the two diagonals are arctan(124/861) and -arctan(124/861) or +/- 8.1953064321025°.

The two hands of a clock are directly opposite one another at 6 o'clock and 10 other times during a 12-hour cycle at 12/11 hour intervals. The angle changes by 360/11 ° each time, or 32.7272727272727°

The angles of the minute hand are

          57.2727272727273
          24.5454545454545
         -8.18181818181819
         -40.9090909090909
         -73.6363636363636
         -106.363636363636
         -139.090909090909
         -171.818181818182
         -204.545454545455
         -237.272727272727
         -270
         -302.727272727273
         
The closest match is -8.181818... matching -8.1953.... This is 3*12/11 hours past 6 o'clock, or          
9:16.3636....

An observer would see a parallelism here.

  Posted by Charlie on 2023-05-12 08:12:03
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