How many times do the hands of a clock overlap in a 12-hour period?

Practice Questions

Q1
How many times do the hands of a clock overlap in a 12-hour period?
  1. 10 times
  2. 11 times
  3. 12 times
  4. 9 times

Questions & Step-by-Step Solutions

How many times do the hands of a clock overlap in a 12-hour period?
  • Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
  • Step 2: Know that the hour hand moves slowly and the minute hand moves quickly.
  • Step 3: Realize that the hands of the clock overlap when they are on top of each other.
  • Step 4: In one hour, the minute hand completes a full circle (60 minutes) while the hour hand moves a little.
  • Step 5: The hands overlap approximately every 65 minutes, but they do not overlap exactly at the start of each hour.
  • Step 6: Count the overlaps: from 12:00 to 1:00, they overlap once, then again from 1:00 to 2:00, and so on.
  • Step 7: Continue counting until you reach 12:00 again, which gives you a total of 11 overlaps in 12 hours.
  • Clock Mechanics – Understanding how the minute and hour hands of a clock move and interact.
  • Time Calculation – Calculating the frequency of events (overlaps) within a given time frame.
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