Multiple choice

At what time between 5.30 and 6 will the hands of the clock be inclined at $90^o$?

  1. $45$ min. past 5
  2. $43 \cfrac{5}{11}$ min. past 5
  3. $43 \cfrac{7}{11}$ min. past 5
  4. $40$ min. past 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 5:30, the angle is 15 degrees. To be 90 degrees apart, the minute hand must gain 75 degrees on the hour hand. The relative speed is 5.5 degrees per minute. Time = 75 / 5.5 = 150/11 = 13 and 7/11 minutes past 5:30. Total time = 30 + 13 and 7/11 = 43 and 7/11 minutes past 5.

AI explanation

Using the formula for the angle between clock hands, |30(H) - 5.5(M)| = 90, we substitute H = 5 to get |150 - 5.5(M)| = 90. This gives two valid equations: 150 - 5.5(M) = 90 and 150 - 5.5(M) = -90. Solving the second equation for the time after 5:30 yields 5.5(M) = 240, so M equals 43 7/11 minutes past 5.

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