At how many distinct points on a watch face do the hour hand and the minute hand meet in a standard 12-hour analogue clock?

A clock shows 3:15. What is the angle between the hour hand and the minute hand?

There are two clocks, both set to show 8:00 pm on Tuesday. One clock gains 3 minutes in an hour and the other clock loses 5 minutes in an hour. By how much time do the two clocks differ at 6:00 pm on Wednesday (the next day)?