At what time between 3:15 and 4:00 are the hands of a clock at right angles?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3:32\(\frac{8}{11}\)
The minute hand gains 5.5° a minute on the hour hand. At 3:00 it is 90° behind the hour hand; the hands are at right angles again when it has passed the hour hand and gone 90° ahead of it.
At 3:00 the hour hand is at 90° and the minute hand at 0°
To be 90° ahead, the minute hand must gain \(90^\circ+90^\circ=180^\circ\)
Minutes needed \(\displaystyle =\frac{180}{5.5}=\frac{360}{11}=32\frac{8}{11}\)
The time is \(32\frac{8}{11}\) minutes past 3, which lies between 3:15 and 4:00
