Multiple choice

The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8:48 am when this angle increases by 50% is

  1. 36 11

  2. 24 11

  3. 2

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 8:48, the hour hand is at 8 + 48/60 = 8.8 hours (264 degrees) and the minute hand is at 48 minutes (288 degrees). The minor angle is 24 degrees. We need the time when the angle becomes 36 degrees. Solving the relative speed equation (5.5 degrees/min) for the change in angle shows the duration is 24/11 minutes.

AI explanation

At 8:48, the minute hand is at 288 degrees and the hour hand is at 264 degrees, making the initial minor angle 24 degrees. For this angle to increase by 50 percent to 36 degrees, the minute hand must gain 12 degrees on the hour hand. Since the relative speed is 5.5 degrees per minute, dividing 12 by 5.5 gives a duration of 24/11 minutes.

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