The Hour Hand and the Minute Hand

             We all know that the hour hand and the minute hand on a clock travel at different speeds .However, there are certain occasion when they are exactly opposite each other. Can you give a simple formula for calculating the times of these occasions?

Answer:   Here is the formula that gives the minutes past twelve to which the hour hand points when the minute hand is exactly thirty minutes ahead.

Minutes Past twelve Y= 30/11[(n-1) 2+1]

Where n is the next hour _

Let’s take the case of at what time between 4 and 5 will the hands be opposite each other? (n=5).

      Y= 3/11 × 9=270/11 + 246/11.               

I.e. the hour hand will be 24 6/11 minutes past 4. The formula may be derived from the following: If X is distance moved by the minute hand y is the distance moved by hour hand.

         Then X-Y = 30

First time the hands move round X= 12 Y

Second time the hands move round X=12 Y- 5                   

Third time the hands move round X= 12 Y-10 etc