At what time between 2 and 3 o’clock are the hands of a clock together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2:10\(\frac{10}{11}\)
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 2:00 the hour hand is at \(2\times30^\circ=60^\circ\) and the minute hand at 0°: a gap of 60°
Minutes needed \(\displaystyle =\frac{60}{5.5}=\frac{120}{11}=10\frac{10}{11}\)
So the hands are together at \(10\frac{10}{11}\) minutes past 2
