How many minutes?

Geometry Level pending

How many minutes after 9 : 00 9:00 o'clock will the hands of the clock be opposite each other for the first time? Round off your answer to two decimal places.


The answer is 16.36.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

If the minute hand moves a distance of x x , the hour hand moves a distance of x 12 \dfrac{x}{12} .

From my figure,

x + 30 = 45 + x 12 x+30=45+\dfrac{x}{12}

x − x 12 = 45 − 30 x-\dfrac{x}{12}=45-30

11 12 x = 15 \dfrac{11}{12}x=15

x = 12 11 ( 15 ) = x=\dfrac{12}{11}(15)= 16.36 m i n \boxed{16.36~min}

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