Calculate the time

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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?

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    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

    John123 Expert Answered on 26th July 2015.
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