An interesting question from a reader:
Dear Mr.. Cramer,
In the bible in Gen.5:32 it says that Noah had lived 500 years, Noah begot Shem, Ham, and Japheth. But in another chapter Gen.7:6 it says that Noah was 600 years old when the flood came. Then you have your forty days and forty nights. and the water swelling on the earth for 150 days then God remembered Noah etc. Then in chapter11 of Gen.11:10 It says that Shem was 100 years old when he begot Arpachshad, two years after the flood. So my Question is have you done any papers on the time discrepancy or do you know were I might be able to find the answer to this interesting Question? Thank you,

This is a problem I hadn't heard before. As I looked at the passages involved, I found two different solutions to this contradiction.
The first solution can be found with Genesis 5:32
And Noah was five hundred years old and Noah begot Shem, Ham, and Japheth.
Unless Noah had triplets we can look at this passage and determine that Noah began to have the first of these three (important) sons at the age of 500.
We can determine that Noah did not have triplets from Genesis 10:21
And children were born also to Shem, …,the brother of Japheth the elder.
The above can also be translated as ",the older brother of Japheth."
So we don't know for certain if Shem was the oldest, middle, or youngest. We do know that there was an age gap between at least two of the brothers mentioned in 10:21
We could conclude from the data that Shem was born when Noah was 502 years old, and Japheth or Ham were born when Noah was 500 years old.
However, there is also a second solution:
What if Shem was the Oldest and born when Noah was 500 years old?
If Noah was 500 when he begot Shem and the Flood occurred when Noah was 600 years old and Shem when 100 years old begot Arphaxad two years after the flood, we have a simple math problem; where did the two years come from?
We know that Noah used a calendar that used 360 days per year.
See: The 360 Day Prophetic Year of the Bible
100 years of 360 days for each year = 36,000 days
Now let's speculate that for Shem a calendar of 365.25 days was used:
100 years of 365.25 days = 36,525 days
36,525 (Shem's calendar )– 36,000 (Noah's calendar) = 525 days difference
If Shem was born when Noah was 500.5 years old then using a 365.25 day Shem would have turned 100 years old 36,705 days after Noah turned 500 (if Noah was using a different calendar). Now we have a difference of 705 days, But Shem would remain 100 years old for another full year until his next birthday;
705 + 365.25 = 1070.25 days difference.
Using a 365.25 day calendar, two years after the flood would be anywhere inbetween 730.5  1095.75 days
If Shem was begot to Noah ½ way through his 500th year and we used the 365.25 day calendar on Shem, then two years after the flood would be anywhere from day 730.5 to day 1095.75. Shem would have been 100 years old from day 705 to day 1070.25. Shem could easily have begot a son at age 100 (365.25 day/year) two years after the flood, it works!
Of course this second theory is pure speculation and we have no bases to use two separate calendars for two different people with the same events, I just found it interesting that it works.
Many strange things happened at this point, such as the flood and the reduction in Mans years to name but a few changes. A change in the time a month and/or year is measured could have taken place during this time. God's decision to reduce the time of man in Genesis 6:3 comes immediately after it mentions that Noah at age 500 begot three sons in Genesis 5:32. Is it just a Coincidence that we may have a calendar discrepancy after this? Was Noah still using the 360 day/year calendar and Shem and others began to follow a different calendar based on changes with the earth caused to shorten the lifespan of men to 120 years. We can only speculate at this time.
Personally, at this point, I would go with the first solution that the brothers were different ages since Genesis 10:21 tells us this. Shem must have been born when Noah was around age 502.
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