On the Second Day: Coincidence problems.

I did these by treating them as problems of pursuit such as are found in elementary algebra texts. In this case the minute hand is chasing after the hour hand.

Example: Find exactly when the two hands coincide after 4:00.

Solution: Let x = distance (in minutes) Hour Hand moves
      Then 12x = distance (in minutes) Minute Hand moves
Position Minute Hand after 4:00
                         = Position Hour Hand after 4:00
The Hour Hand has a 20-minute head start
12x = 20 + x
11x = 20
x = 20/11 = 1 9/11 
12x = 12(1 9/11) = 12 108/11 = 21 9/11

So the hands coincide at exactly 4:21 9/11

(Compare this result to the approximation above.)

All Coincidence problems have this basic form.

Problem 1: Find exactly when the two hands coincide after 9:00.    nine forty eight

(Answer:  9:49 1/11)