Between 4 and 5 o'clock, at what time will the dashed 3–9 line exactly bisect the angle between the hands?

Symmetry about the 3–9 line means the two angles from 12 add up to $180^{\circ }:(120+\frac{m}{2})+6m=180$, so $6.5m=60$ and $m=\frac{120}{13}=9\frac{3}{13}.(10\frac{10}{11}$ uses the relative speed 5.5 instead of the sum 6.5.)