Multiple choice

At what time between $7$ and $8$ o' clock will the hands of a clock be in the same straight line but, not together?

  1. $5$ min. past $7$
  2. $5\displaystyle\frac{2}{11}$ min. past $7$
  3. $5\displaystyle\frac{3}{11}$ min. past $7$
  4. $5\displaystyle\frac{5}{11}$ min. past $7$
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D Correct answer
Explanation

At 7 o'clock, the hands are 35 minute spaces apart. For them to be in a straight line but not together, they must be 30 minute spaces apart. The minute hand must gain 35 - 30 = 5 minute spaces. The time taken is 5 * (60/55) = 60/11 = 5 5/11 minutes past 7.

AI explanation

Using the clock angle formula for a straight line not together, the minutes past 7 equals (60 * 7 - 180) * (2 / 11). This calculates to 240 * (2 / 11), resulting in 480 / 11 or 5 and 5/11 minutes past 7.

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