Some time after 2 o’clock and before 3 o’clock, the hour hand and the minute hand of a clock make a straight angle (180°). At what time does this happen?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 43\(\frac{7}{11}\) minutes past 2
Measured from 12, the minute hand turns 6° a minute and the hour hand 0.5° a minute, so the minute hand gains 5.5° a minute. For a straight angle it must get 180° ahead of the hour hand.
At 2:00 the hour hand is at \(2\times30^\circ=60^\circ\) and the minute hand at 0°: the minute hand is 60° behind
It must gain \(60^\circ+180^\circ=240^\circ\)
Minutes needed \(\displaystyle =\frac{240}{5.5}=\frac{480}{11}=43\frac{7}{11}\)
So the hands point in opposite directions at \(43\frac{7}{11}\) minutes past 2
