NOTE: For a thousand years, people have claimed to have found "Noah's Ark".  Some say that it is 4500 years old others, 10,000. According to the Bible, the ark was made of wood, Why would any suppose that a wooden object would survive for more that 4000 years? If the Earth had been completely flooded and they were trapped on a mountain top, wouldn't they have used the wood of the ark to light fires and to construct tools and homes? It is nonesense to assume that any large part of the ark would survive to this day.

There are similar Deluge stories to be found thoughout the middle East, Asia and Africa. All these stories have the elements of a named man building a box, putting many animals in it and surviving a great flood with his family. 

In Genesis we find the story of Noah and his ark (a box), Zoroastrian scriptures tell of Yima and his vara ( a large square enclosure),  the Sumerians wrote about Ziusudra and his great ship, in Southwestern China we find the story of Du-mu and his hollowed out log, in New Hebrides there is Qat and his great canoe, Michoacan people tell of Tezpi and his great vessel, the Masai have the legend of Tumbainot who built an ark of wood, the Loyalty Islanders have Nol and his canoe, there is the Hindu lengend of King Manu and his great boat, the Hawaiians relate the story of Nu'u, in Eastern Siberia we hear of Noj and the iron vessel of God,  The ancient Assyrian scriptures speak of Utnapishtim who built a large boat, the Babylonian records relate the story of Atrahasis whu built an ark (box), and then there are the Chaldeans with their story of Xisuthrus and his giant vessel.

First, we should note that an ark is not a boat but a box, no matter what you have seen illustrated.

Secondarily, noah did not land on Mt. Ararat. He landed on "the hills of Ararat". Ararat has been identified as the territiory south east of the Black Sea in Eastern Turkey. If all the glaciers in the world were to meltm and the Mediterraen Sea empty itself into the Black Sea, the water level of the Black Sea would only raise about 300 feet or so, not the 1300 feet necessary to place it atop  the modern Mt. Ararat.

 
Here is what likely happened:

Sometime before 5000 BC, Noah was living aling the Southeastern border of the Black Sea. This was home to a growing civilzation with vast farmklands, many growing town and much commerce. Through revelation from God, intuition, or reports from travellers, realized that an ice dam, or bockage to the north was about to give way

He built a large raft, put walls and a roof on it, maybe a couple of decks, and moved in his farm animals(perhaps a hundred), food and animal feed.  The family (maybe a dozen people or so) lived on board the raft until the dam broke. The raft floated and drifted eastward to finally come to rest on some of the higher hills in Ararat., maybe 200 or 300 feet higher than where he had once lived- and maybe fifty miles eastward.

He survived when thousands perished. It was quite an adventure and the story was passed on down to his descendants as they spread south and eastward to what became Sumeria, Babylon and Assyria