Discussion

At what time between 2 and 3 o'clock will the hands of a clock be together?

Answer: B

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

Together means \( \theta = 0 \), with \( H = 2 \):

\[ 5.5M = 60 \quad\Longrightarrow\quad M = \frac{120}{11} = 10\tfrac{10}{11} \]

So the hands meet at \( 10\tfrac{10}{11} \) minutes past 2.

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