Multiple choice

At what time between 4 o'clock and 5 o'clock will the two hands of the clock be at the right angle to each other for the first time?

  1. $58/11 min past 4 o'clock$
  2. $422/11 min past 4 o'clock$
  3. $60/11 min past 4 o'clock$
  4. $420/11 min past 4 o'clock$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 4:00, the hour hand is at 120° from 12 and minute hand at 0°. The relative speed is 5.5°/min. For the first right angle (90°), we solve |120 - 5.5t| = 90. This gives 5.5t = 30, so t = 60/11 minutes past 4 o'clock.

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