Multiple choice

At what time between 4 o'clock and 5 o'clock will the minute hand of a clock be 78° behind the hour hand?

  1. 5 6 11 min past 4

  2. 7 7 11 min past 4

  3. 9 5 11 min past 4

  4. 105/11 min past 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At m minutes past 4, the hour hand is at 120 + 0.5m degrees and the minute hand is at 6m degrees. Since the minute hand is 78 degrees behind, 120 - 5.5m = 78, giving m = 84/11 = 7 7/11 minutes.

AI explanation

Using the clock angle formula Theta equals 30H minus 11M/2, we substitute the angle of 78 degrees and the hour of 4. This yields the equation 78 equals 120 minus 11M/2. Solving for M gives 11M/2 equals 42, which means M equals 84/11 or 77/11 minutes past 4.

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