Calculate the time
We all know that the hour hand and the minute hand on a clock travel at different speeds. However there are certain occasions when the hands are exactly opposite each other. Can you give a simple formula for calculating the times of these occasions?
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=30/11 x9 =270/11 . i.e. the hour hand will be 270/11 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
Your Answer
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