Overall timespan of the Patriarchs
The flood was about 1650 years after the original creation. Abraham was born about 300 years after the flood, and a little under 2000 years after creation.
The genealogies are consistent in themselves, without contradictions. The genealogies are also consistent with the other genealogies in the Bible, including those in the Book of Chronicles (1 Chr 1:1-24), and the Gospel of Luke (Lk 3:34-38). In the Book of Jude, Enoch is “in the seventh generation from Adam” (Jude 14), which matches Genesis (5:1-20).
Decrease of lifespans after the flood
There was a dramatic decrease of lifespan following the flood. Before the flood, most of the patriarchs lived around 900 years, but after the flood this reduced rapidly to 200 years or under. This matches the statement made by God in connection with the rather strange account of the sons of God and the daughters of men. “Then the LORD said, ‘My spirit shall not abide in mortals forever, for they are flesh; their days shall be one hundred and twenty years.” (Gen 6:3). It was this great wickedness that led God to send the flood (6:7).
Later, when the Pharaoh of Egypt asked Jacob how old he was, Jacob compared his short life of 130 years with the long lives of the patriarchs. “Jacob said the Pharaoh, ‘The years of my earthly sojourn are 130; few and hard have been the years of my life. They do not compare with the years of the life of my ancestors during their long sojourn’” (Gen 47:9). It would imply the life after the flood was far harsher than before.
Lamech’s life overlapped all the patriarchs from Adam to Noah. Adam was the six times great grandfather of Lamech. He was living at the same time as all patriarchs before flood. He would know their lifespans and many details of their lives.
Enoch's life was only about a third as long as the other patriarchs. This explanation is given, "Enoch walked with God; then he was no more, because God took him" (5:24). He is listed among the heroes of faith in the Book of Hebrews, "By faith Enoch was taken so he did not experience death; and 'he was not found, because God had taken him'. For it was attested before he was taken away that 'he had pleased God'" (Heb 11:5).
Methuselah’s name means something like, ‘when he dies, judgement’. He was the longest living of all the patriarchs - 969 years, and eventually died in the year of the flood. His life and name is a powerful statement of God’s grace and reluctance to judge. God was willing to wait almost a thousand years before sending judgement, in the hope that people will repent.
Noah, together with his three sons (and the four wives), are the only ones of the patriarchs to survive the flood. All the pre-flood patriarchs had already come to the end of their lives. "... Noah, during the building of the ark, in which a few, that is, eight persons, were saved through water". (1 Pet 3:20). All the generations following Shem were born after the flood.
Shem actually outlived all but one of the following nine generations, including Abraham, his seven times great grandson. Jewish tradition identifies Shem as Melchizedek, “And Malka Zadika, who was Shem bar Noah, the king of Yerushalem, came forth to meet Abram, and brought forth to him bread and wine; and in that time he ministered before Eloha Ilaha. (And Malki Zedek, king of Yerushalem, who was Shem, who was the great priest of the Most High.) And he blessed him, and said, Blessed be Abram of the Lord God Most High, who for the righteous possesseth the heavens and the earth. And blessed be Eloha Ilaha, who hath made thine enemies as a shield which receiveth a blow. And he gave to him one of ten, of all which he brought back.” (Targum Pseudo-Jonathan on Genesis 14:8)
When returning from the war of the kings, Abraham was met by Melchizedek who blessed him. “And King Melchizedek of Salem brought out bread and wine; he was a priest of God Most High. He blessed him and said, ‘Blessed be Abram by God Most High, maker of heaven and earth; and blessed be God Most High, who has delivered your enemies into your hand!’”
Melchizedek’s name means 'king of righteousness', and he was king of Salem, that is king of peace (Heb 7:2). This suggests that Melchizedek is a title, rather than a name, making it quite possible that he can be identified as Shem.
Eber outlived the next six generations, including Abraham. The Hebrew people were named after him, being known as the 'children of Eber', or Hebrews (10:21, 14:13).
Peleg’s name means ‘division’, “for in his days the earth was divided” (10:25). This probably
refers to the scattering of the nations following the Tower of Babel (Gen 11). This would suggest that the Tower of Babel was about 100 years after the flood.
Differences in the Septuagint
There are some significant differences between the Hebrew text for the genealogies in Genesis chapter 11 and the Greek Septuagint. The Septuagint regularly adds 100 years to the ages of Shem's line (Gen 11) when they had a son, while the age at the death of each patriarch remains the same.
At the time of Jesus the Greek Septuagint was the commonly used version of the Scriptures (our OT). The NT quotations of the OT are normally from the Septuagint, which accounts for minor differences when compared with the passages being quoted in the OT.
The main manuscripts used to translate the Book of Genesis today are the Samaritan Pentateuch, from about the first century AD, the Masoretic text from around the 9th century AD, and the Septuagint, translated into Greek around 250 BC. Fragments of the Book of Genesis were discovered in the Dead Sea Scrolls, but those do not include chapter 11. It appears that there are more similarities between the Septuagint and the Samaritan Pentateuch. Both have the extra 100 years before the birth of the son of seven of the patriarchs between Arpachshad and Nahor, which are not there in the Masoretic text.
The Septuagint would have been translated from an earlier Hebrew manuscript (from before 250 BC). In the process of textual criticism, earlier manuscripts are normally considered to be more accurate than more recent ones. However, when the Dead Sea Scroll of Isaiah (dated between the second century BC and the first century AD) was compared with the Masoretic text from nearly 1000 years later, there were very few minor differences in the text, so the Masoretic text is normally considered to be quite accurate.
Where there are differences, this would suggest that the Septuagint and Samaritan Pentateuch versions are more likely to be correct, or at least be closer to the original text, than the Masoretic text, so the extra hundred years should probably be included.
Josephus also would have used the Septuagint as his source, so he included the extra hundred years (Ant 1.6.5).
The Septuagint also adds an additional generation of Cainan, between Arpachshad and Shelah (v12-13), who is also included in Luke's genealogy of Jesus (Lk 3:6). Luke would have used the Septuagint as his source. Cainan does not appear in the genealogy in 1 Chronicles (1:17ff), or the Samaritan Pentateuch, so there is no easy way to decide whether he should be included or not. Cainan is not included by Josephus or by the Septuagint translation of 1 Chronicles (1 Chr 1:27). Perhaps he was included accidentally in the Septuagint translation of Gen 11.