A factory's day shift runs from the time on clock A (morning) to the same time on clock B (evening). How many times do the hour and minute hands coincide during the shift?

The minute hand gains $360^{\circ }$ on the hour hand every $\frac{360}{5.5}=65\frac{5}{11}$ min, so in 12 hours the hands meet $\frac{720}{65\frac{5}{11}}=11$ times: not every hour, because the meeting between 11 and 1 happens only once, at 12:00 (noon). (12 assumes one meeting each hour; 22 is for a full day.)