Between 9 o’clock and 10 o’clock, at what time does the minute hand of a clock pass exactly over the hour hand?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 49\(\frac{1}{11}\) minutes past 9
The minute hand turns 6° a minute and the hour hand 0.5° a minute, so the minute hand gains 5.5° a minute on the hour hand. The hands are together when this gain closes the gap between them.
At 9:00 the hour hand is at \(9\times30^\circ=270^\circ\) from 12 and the minute hand at 0°: gap \(=270^\circ\)
Minutes needed to close the gap \(\displaystyle =\frac{270}{5.5}=\frac{540}{11}=49\frac{1}{11}\)
So the hands are together at \(49\frac{1}{11}\) minutes past 9
