Question

How long after 7:30 are a clock's minute hand and hour hand 50 degrees apart? The answer is 17.3 minutes, but I don't know how to get it. Help!

Answer 1

I takes a minute hand 60 minutes to go 360 degrees or 6 degrees per minute. It takes an hour hand 12*60=720 minutes to go 360 degrees or .5 per minute. At 7:30, the minute hand is pointing exactly on the 6 and the hour hand is half-way between the 7 and the 8; an angle of 45 degrees. Since the minute hand is behind the hour hand, lets make the angle -45 degrees.

Ok, solve for minute m where -45 + 6m - .5m = 50.

I get m=17.25 which rounds to 17.3 minutes.