At what time between 8 and 9 o’clock are the hands of a clock together?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8:43\(\frac{7}{11}\)
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 8:00.
At 8:00 the hour hand is at \(8\times30^\circ=240^\circ\) and the minute hand at 0°: a gap of 240°
Minutes needed \(\displaystyle =\frac{240}{5.5}=\frac{480}{11}=43\frac{7}{11}\)
So the hands are together at \(43\frac{7}{11}\) minutes past 8
