Between 3 and 4 O'clock, both hour hand and minute hand will coincide past 3 O'clock between

Explanation

At 3:00, the minute hand is 15 minute-spaces behind the hour hand. To coincide, it must gain 15 minute-spaces. Since it gains 55 minute-spaces in 60 minutes, time taken = 15 \times \frac{60}{55} = \frac{180}{11} = 16 \frac{4}{11} minutes. This is between 16 and 17 minutes.

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