At what time between 7 and 8 o'clock will the hands of a watch point in opposite directions?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(5\frac{5}{11}\) min past 7
The minute hand turns 6° a minute and the hour hand 0.5° a minute, so the minute hand gains 5.5° on the hour hand every minute. The hands point in opposite directions when they are 180° apart.
At 7:00 the hour hand is at \(7\times30=210\)° and the minute hand at 0°: the minute hand is 210° behind.
For the hands to be opposite, the gap must fall to 180°, so the minute hand must gain \(210-180=30\)°.
Time taken: \(\displaystyle\frac{30}{5.5}=\frac{60}{11}=5\frac{5}{11}\) minutes
