Discussion
At what time between 10 and 11 o’clock will the hands of a clock coincide ?
Answer: D
Correct answer: 54 (6/11) min past 10
At 10 o’clock the hour hand leads the minute hand by \(300°\), and the minute hand gains \(5.5°\) per minute.
\[t = \frac{300}{5.5} = \frac{600}{11} = 54\tfrac{6}{11}\ \text{minutes}\]
So they coincide at \(54\tfrac{6}{11}\) minutes past 10, the last coincidence before the hands meet again at 12.
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