Starting exactly at 1:00 PM, how many times will the minute hand and the hour hand of a clock form an angle of 40° with each other over the next 6 hours (i.e., until 7:00 PM)?

What is the angle between the hour hand and the minute hand of a clock at 12:55?

There are two clocks, both set to show 10 p.m. on 21st January, 2010. One clock gains 2 minutes in an hour and the other clock loses 5 minutes in an hour. By how many minutes do the two clocks differ at 4 p.m. on 22nd January, 2010?