12 hours on the clock makes a 360 degree circle. So each hour is 30 degrees (360/12). The hour hand will be directly on the 3 when the minute hand is at 12 (3:00). After 15 minutes or 1/4 of an hour, the hour hand will be 1/4 * 30 deg = 7.5 degrees away from the minute hand.
Both hands start at 12, and the minute hand will pass the hour hand each hour after that. When the hour hand is at 11, the minute hand wil come around and pass the hour hand for the eleventh time. The final time around, they will end up on the 12 at the exact same moment. So the minute hand passes the hour hand 11 times every 12 hours, so it must pass it every 1 and 1/11 hours (12/11 hours).