Quandaries and Queries 

Following is my question for you. When you are looking at the clock at 12:00 the hour hand and minute hand are exactly together. (one on top of the other). Between 1:00pm and 1:15pm there is another time when the hour and minute hands are exactly together again. I need to know what time this is and is there a formula that can be used to figure it out? Thanks so much for your help
Student Hi Minnie, The minute hand moves 360 degrees in 60 minutes and hence it moves at a rate of ^{360}/_{60} = 6 degrees per minute. The hour hand moves 360 degrees in 12 60 minutes and hence it moves at a rate of ^{360}/_{12 60} = ^{1}/_{2} a degree per minute. Thus, t minutes after 12:00 the minute hand has moved 6t degrees and the hour hand has moved ^{t}/_{2} degrees. Hence the angle between the hands is Penny 

