(related to Problem: The Club Clock)
The positions of the hands shown in the illustration could only indicate that the clock stopped at $44$ min. $51\frac{1143}{1427}$ sec. after eleven o'clock. The second hand would next be "exactly midway between the other two hands" at $45$ min. $52\frac{496}{1427}$ 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. $22\frac{106}{1427}$ 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.
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