Discussion

The minute hand and hour hand of a clock meet every 62 minutes. Does the clock gain or lose in 24 hours. And how much does it lose or gain?

Answer: C

In a correct clock the hands coincide every

\[ \frac{720}{11} = 65\tfrac{5}{11} \text{ minutes} \]

Here they coincide every 62 minutes, sooner than they should, so the clock is gaining.

\[ \text{gain per interval} = \frac{720}{11} - 62 = \frac{38}{11} \text{ min} \]

In 1440 minutes there are \( \tfrac{1440}{62} \) such intervals:

\[ \text{gain per day} = \frac{38}{11} \times \frac{1440}{62} = \frac{54720}{682} = 80\tfrac{80}{341} \text{ minutes} \]

Coinciding more often than every \( 65\tfrac{5}{11} \) minutes always means a fast clock; a slower interval, such as 64 minutes, would mean a loss.

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