How many times in a day are the hands of a clock pointing opposite to each other?
Step-by-step Solution:
1. The Basic Logic The hands of a clock point opposite to each other when they form a straight line (a 180° angle). This event happens roughly once every hour.
2. Occurrences in a 12-Hour Period - It might seem like the hands should be opposite 12 times in 12 hours, but there is an exception.
- Between 5:00 and 7:00 (a two-hour window), the hands are opposite only once, exactly at 6:00. The event that would typically happen in the 5 o'clock hour occurs at the 6 o'clock mark instead.
- Because of this single "skipped" event, the hands point opposite to each other only 11 times in a 12-hour period.
3. Occurrences in a 24-Hour Period (a day) - A full day has two 12-hour cycles.
- Total occurrences = (Occurrences in 12 hours) × 2
- Total occurrences = 11 × 2 = 22 times.
Final Answer: The hands of a clock point opposite to each other 22 times in a day.