At what time between 10 and 11 o’clock are the hands of a clock together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10:54\(\frac{6}{11}\)
The minute hand turns 6° a minute and the hour hand 0.5°, so the minute hand gains 5.5° a minute. The hands are together when the minute hand has made up the whole gap it starts with.
At 10:00 the hour hand is at \(10\times30^\circ=300^\circ\) and the minute hand at 0°: a gap of 300°
Minutes needed \(\displaystyle =\frac{300}{5.5}=\frac{600}{11}=54\frac{6}{11}\)
So the hands are together at \(54\frac{6}{11}\) minutes past 10
