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Zorluk: Çok zorClocks and Calendars

Clock A continuously loses 22 minutes every hour, while Clock B continuously gains 11 minute every hour. Both clocks are synchronized to the exact true time at 8:00 AM on Monday, February 26, 1900.

Which of the following represents the exact day of the week, calendar date, and the time displayed by Clock B at the earliest instance when the time displayed by Clock A and Clock B are exactly 1212 hours apart?

  1. A
    Thursday, March 7, 1900, at 12:00 Noon
  2. B
    Thursday, March 8, 1900, at 8:00 AM
  3. Thursday, March 8, 1900, at 12:00 NoonCevap
  4. D
    Wednesday, March 7, 1900, at 12:00 Noon

Cevap

Thursday, March 8, 1900, at 12:00 Noon
The two clocks drift apart at a combined rate of 3 minutes per hour. To achieve a 12-hour (720-minute) difference, exactly 240 true hours (10 days) must pass. Since 1900 is not a leap year, February has 28 days. Advancing 10 days from Monday, February 26 brings the true date to Thursday, March 8. In those 240 hours, Clock B gains 240 minutes (4 hours). Since the true time is 8:00 AM, Clock B displays 12:00 Noon.

Adım Adım Çözüm

1
Calculate the relative speed of separation between the two clocks.
Clock A loses 2 mins/hr and Clock B gains 1 min/hr. Relative separation = 2 + 1 = 3 minutes every hour.
Since they move in opposite directions relative to the true time, their rates are added to find how fast they drift apart.
2
Determine the true time required for the clocks to be 12 hours apart.
12 hours = 720 minutes. Time required = 720 / 3 = 240 hours. 240 hours = 10 full days.
Dividing the total required separation by the hourly separation rate yields the total elapsed true time.
3
Calculate the true calendar date and day of the week after 10 days.
The year 1900 is not a leap year, so February has 28 days. Starting from Feb 26, adding 2 days reaches Feb 28. The remaining 8 days land on March 8. Monday + 10 days (or Monday + 3 odd days) = Thursday.
Century years must be divisible by 400 to be leap years. 1900 does not meet this condition.
4
Determine the time displayed by Clock B after 240 hours.
Clock B gains 1 minute per hour. In 240 hours, it gains 240 minutes, which is exactly 4 hours. True end time is 8:00 AM. 8:00 AM + 4 hours = 12:00 Noon.
The question specifically asks for the time displayed by Clock B, not the true time.

Anahtar Kavram

Relative speed of faulty clocks combined with century leap year constraints.
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Clocks and Calendars

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