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.
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 12hour 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 20230512 08:12:03 