Multiple choice

After $\text{9 o ' clock}$ at what time between $\text{9 p.m. and 10 p.m.}$ will the hour and minute hands of a clock point in opposite direction ?

  1. $\text{15 minutes past 9}$
  2. $\text{16 minutes past 9}$
  3. $16\displaystyle\frac{4}{11}\,\text{minutes past 9}$
  4. $17\displaystyle\frac{1}{11}\,\text{minutes past 9}$
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C Correct answer
Explanation

At 9 o'clock, the hands are 45 minutes apart. To be opposite, the minute hand must gain 15 minutes on the hour hand. Time = (15 * 60) / 55 = 900 / 55 = 180 / 11 = 16 and 4/11 minutes past 9.

AI explanation

Using the formula for opposite directions, we calculate (180 + 270) divided by 5.5. This gives 450 divided by 5.5, which equals 4500 divided by 11. This results in 16 and 4/11 minutes past 9 o'clock.

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