If you look at a clock and the time is 3 hours 15 minutes what is the angle between the hour and the minute hands?

It should be 7.5°.

The hour hand continues to move, although at a slower pace than the minute hand.

From 3:00 to 3:15, the hour hand will move one-fourth of the distance from the "3" to the "4". In an hour, the hour hand moves one-twelfth of a circle. So in 15 minutes, the minute hand will arrive at the "3" and the hour hand will have moved one-fourth of one-twelfth of 360° - which is 7.5° - past the "3".