Club Watch
Answer :

The positions of the hands shown in the illustration could only indicate that the clock stopped at 44 min. 511143/1427 sec. after eleven o'clock.
The second hand would next be "exactly midway between the other two hands" at 45 min. 52496/1427 sec. after eleven o'clock.
If we had been dealing with the points on the circle to which the three hands are directed, the answer would be 45 min. 22106/1427 sec. after eleven; but the question applied to the hands, and the second hand would not be between the others at that time, but outside them.

Math Genius