At what time between 1 and 2 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) → 1:38\(\frac{2}{11}\)
In a straight line but not together means the hands point opposite ways, 180° apart. Measured from 12, the hour hand is at \(30^\circ+0.5^\circ\) per minute after 1 and the minute hand at \(6^\circ\) per minute.
At 1:00 the hour hand is at 30° and the minute hand at 0°: the minute hand is 30° behind
Each minute the minute hand gains \(6^\circ-0.5^\circ=5.5^\circ\) on the hour hand
To point the opposite way it must catch up the 30° and then get 180° ahead, a gain of \(30^\circ+180^\circ=210^\circ\)
Minutes needed \(\displaystyle =\frac{210}{5.5}=\frac{420}{11}=38\frac{2}{11}\)
So the time is \(38\frac{2}{11}\) minutes past 1
