At what time between 9 and 10 o’clock will the hands of a clock be in the same straight line but not together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9:16\(\frac{4}{11}\)
In a straight line but not together means the hands point opposite ways, 180° apart. Measured from 12, the hour hand is at \(270^\circ+0.5^\circ\) per minute after 9 and the minute hand at \(6^\circ\) per minute.
At 9:00 the hour hand is at 270° and the minute hand at 0°: the minute hand is 270° behind
Each minute the minute hand gains \(6^\circ-0.5^\circ=5.5^\circ\) on the hour hand
The gap must come down from 270° to 180°, a gain of \(270^\circ-180^\circ=90^\circ\)
Minutes needed \(\displaystyle =\frac{90}{5.5}=\frac{180}{11}=16\frac{4}{11}\)
So the time is \(16\frac{4}{11}\) minutes past 9
