SOLUTION: By 5:40 pm, through how many degrees has a clock's hour hand moved since noon?

Every hour, the hour hand rotates   = 30 degrees.


In 5 hours, the hour hand rotates 5*30 = 150 degrees.


40 minutes is    of an hour, so 40 minutes contribute   degrees = 20 degrees.


Therefore, the total angle of rotation at 5:40 pm will be 5*30 + 20 = 150+20 = 170 degrees, since noon.