The positions of the hands shown in the illustration could only indicate
that the clock stopped at 44 min. 51+1143/1427 sec. after eleven
o'clock. The second hand would next be "exactly midway between the other
two hands" at 45 min. 52+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+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.