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In which months are the day and the night the same length? Which month has the longest day? Which month has the shortest day? Find the difference hours and minutes between the longest day and night for each date in the table above.

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps

To find the length of day, we subtract the sunrise time from the sunset time. To find the length of night, we subtract the length of day from 24 hours.

  1. Calculate Length of Day and Night for March 23

    Sunrise: 6:53 am, Sunset: 6:53 pm
    Length of day: From 6:53 am to 6:53 pm is exactly 12 hours.
    Length of night:

    24 hours−12 hours=12 hours24 \text{ hours} - 12 \text{ hours} = 12 \text{ hours}
    • Length of day: 12 hours 0 minutes
    • Length of night: 12 hours 0 minutes
  2. Calculate Length of Day and Night for June 21

    Sunrise: 7:50 am, Sunset: 5:26 pm
    Length of day:
    From 7:50 am to 12:00 pm = 4 hours 10 minutes
    From 12:00 pm to 5:26 pm = 5 hours 26 minutes
    Total length of day = (4 hours + 5 hours) + (10 minutes + 26 minutes) = 9 hours 36 minutes.
    Length of night:

    24 hours−9 hours 36 minutes24 \text{ hours} - 9 \text{ hours } 36 \text{ minutes} =23 hours 60 minutes−9 hours 36 minutes= 23 \text{ hours } 60 \text{ minutes} - 9 \text{ hours } 36 \text{ minutes} =(23−9) hours (60−36) minutes= (23-9) \text{ hours } (60-36) \text{ minutes} =14 hours 24 minutes= 14 \text{ hours } 24 \text{ minutes}
    • Length of day: 9 hours 36 minutes
    • Length of night: 14 hours 24 minutes
  3. Calculate Length of Day and Night for September 22

    Sunrise: 6:10 am, Sunset: 6:10 pm
    Length of day: From 6:10 am to 6:10 pm is exactly 12 hours.
    Length of night:

    24 hours−12 hours=12 hours24 \text{ hours} - 12 \text{ hours} = 12 \text{ hours}
    • Length of day: 12 hours 0 minutes
    • Length of night: 12 hours 0 minutes
  4. Calculate Length of Day and Night for December 22

    Sunrise: 5:39 am, Sunset: 7:08 pm
    Length of day:
    From 5:39 am to 12:00 pm = 6 hours 21 minutes
    From 12:00 pm to 7:08 pm = 7 hours 8 minutes
    Total length of day = (6 hours + 7 hours) + (21 minutes + 8 minutes) = 13 hours 29 minutes.
    Length of night:

    24 hours−13 hours 29 minutes24 \text{ hours} - 13 \text{ hours } 29 \text{ minutes} =23 hours 60 minutes−13 hours 29 minutes= 23 \text{ hours } 60 \text{ minutes} - 13 \text{ hours } 29 \text{ minutes} =(23−13) hours (60−29) minutes= (23-13) \text{ hours } (60-29) \text{ minutes} =10 hours 31 minutes= 10 \text{ hours } 31 \text{ minutes}
    • Length of day: 13 hours 29 minutes
    • Length of night: 10 hours 31 minutes

    Here is the completed table:

    DateSunriseSunsetLength of dayLength of night
    March 236:53 am6:53 pm12 hours 0 minutes12 hours 0 minutes
    June 217:50 am5:26 pm9 hours 36 minutes14 hours 24 minutes
    September 226:10 am6:10 pm12 hours 0 minutes12 hours 0 minutes
    December 225:39 am7:08 pm13 hours 29 minutes10 hours 31 minutes
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