Discussion
At what time between 4 and 5 o’clock will the hands of a clock first be at right angles ?
Answer: D
Correct answer: 5 (5/11) min past 4
At 4 o’clock the hour hand leads by \(120°\). For the first right angle the minute hand must reduce that lead to \(90°\), a relative gain of \(30°\).
\[t = \frac{30}{5.5} = \frac{60}{11} = 5\tfrac{5}{11}\ \text{minutes}\]
The second right angle in that hour comes when the minute hand has gained \(210°\), at \(38\tfrac{2}{11}\) minutes past 4.
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