the minute hand of a clock makes 1 revolution in an hour, so it moves through 360 every hour. the hour hand only 1/12 of revolution in an hour, so it moves through 30 every hour. if i let t represent the time (in hours) since 12:00 then 360t represents the number of degrees through which the minute hand moves and 30t represents the number of degrees through which the hour hand moves. when the minute hand catches up with the hour hand for the first time, it was completed 1 revolution more than the hour hand, so i must subtract 1 from 360t before setting it equal to 30t l. so, 360t - 1 = 30t