what's the time .?

Algebra Level pending

How many minutes after 9:00 PM will the minute hand of the clock overtakes the hour hand? Give your answer as decimal number rounded to two decimal places.


The answer is 49.09.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

If the minute hand moves x x minutes, the hour hand moves x 12 \dfrac{x}{12} minutes. From the diagram, we have

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

x − x 12 = 45 x-\dfrac{x}{12}=45

x = 540 11 ≈ 49.09 m i n u t e s x=\dfrac{540}{11} \approx \boxed{49.09~minutes}

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