Noah was six hundred year's old when the floodwaters came on the earth. The flood has been dated to about 5,000 years ago (actually, about 4,950 years ago, see "Time, Life, and History in the Light of 15,000 Radiocarbon Dates", Whitelaw, 1970, or the updated paper "The biblical record of Creation, Flood and history in light of 30,000 radiocarbon dates", Proceedings, 15th Anniversary Convention of Bible Science Association, pp. 197-202, 1979). The given verses document key events during the year-long flood.

Note that God had the animals and people board the ark seven days before the start of the flood. This would acclimate the animals to their temporary home before the rough environment of the flood began.

Also note that God kept them on the ark for three months (Dec, Jan, Feb) following the first appearance of dry land in order to give time for plants to grow to provide food for the animals.