At what time between 6 and 7 o’clock are the hands of a clock together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6:32\(\frac{8}{11}\)
The minute hand gains 5.5° a minute on the hour hand (6° against 0.5°). The hands are together when it has made up the gap it starts with at 6:00.
At 6:00 the hour hand is at \(6\times30^\circ=180^\circ\) and the minute hand at 0°: a gap of 180°
Minutes needed \(\displaystyle =\frac{180}{5.5}=\frac{360}{11}=32\frac{8}{11}\)
So the hands are together at \(32\frac{8}{11}\) minutes past 6
