Wednesday, September 25, 2013

EQUINOX PROBLEM SOLUTION

Yesterday, the sun rose at 7:02 AM and set at 7:06 PM. Today it rose at 7:04 AM. How long was the day on September 24 and how long was the night of September 24-25?

Note that the colon between hours and minutes is not a decimal point; time uses base 60. One each side of the colon, you can use decimal arithmetic. Working with time is a little tricky!

Day: use 24 hour clock, add 12 to PM hours. So, sun sets at 19:06. 19:06 - 7:02 = 12:04
Night: how much time between sunset and midnight? 12:00 - 7:06. You can't subtract :06 from :00, so "borrow" 60 minutes from the hour of midnight: 11:60 - 7:06 = 4:54. Now add the time until sunrise:
4:54 + 7:04 = 11:58.

The day is 12 hours and 4 minutes long and the night is 11 hours and 58 minutes long. These don't add up to 24 because we are looking at two different days. We are near the autumnal equinox so the day and night are approximately equal to 12 and approximately equal to each other.

As time goes on, days will get shorter and nights longer until the winter solstice, in December.

Today, the sun rises at 7:04 AM and sets at 7:04 PM, so the day is exactly 12 hours.Tomorrow, the sun will rise at 7:05 AM, the night is longer than the day: prove this!

You will find the night is 11 hours and 61 minutes, so change 61 minutes to an hour and one minute.

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