Mehul's afternoon shift at a call centre runs from the time on clock A to the time on clock B. How many times are the clock's hands at right angles during the shift?

A shows 1:00 and B shows 5:30. Right angles occur at $\frac{90+180k}{5.5}$ min past 12: about 1:22, 1:55, 2:27, 3:00, 3:33, 4:05, 4:38 and 5:11 lie inside, and 5:44 is too late. That is 8. (9 counts two per hour for 4.5 hours.)