It would be natural for the scholars who formulated the mathematics of the Deluge to ask the question of how the height of the water of the Deluge compares with the highest mountains. This leads to an explanation of how Mount Ararat came to be mentioned in the story.
Let us follow the strand of the version according to which the water rose for 150 days. This implies that the water rose 150 cubits a day, since 150 x 150 = 22,500. Genesis (8:1-3) tells us that the rise of the waters lasted 150 days and after that they receded "at a steady rate" as it is stated twice for the sake of clarity. But after these verses the same information is repeated, stating that the flood of water stopped after 150 days and it is explained further than this happened on the seventeenth day of the seventh month.
The third hand in its effort to spell out the story added verse 8:4: "On the seventeenth day of the seventh month the Ark came to rest on the mountain of Ararat." The text very deliberately says "came to rest," i.e., "became still." The interpretations and translations to the effect that the Ark "grounded on the mountain of Ararat" are unwarranted, since the verb ~~~~ cannot have that meaning. The original version must have said or implied that the Ark first touched ground on the mountain of Ararat, because that is where land began to emerge under the Ark; then ground continued to emerge under and around the Ark. It must be kept in mind that the Ark itself is a model of the northern hemisphere. The third hand, which followed the second version according to which the water rose for 150 days and ebbed for 150, could not assume that the Ark grounded on the 151st day, because the traditional place of landing of the Ark was by far exceeded by the height of the waters of the flood -- 22,500 Roman cubits above sealevel. Hence, it stated that on the 151st day the Ark, after having been tossed by the waters, stopped at a point which was above the place where it would land later, as the water receded. The writers of the third hand had created a real difficulty for themselves by trying to be specific, because there was not a mountain high enough to fit their version of the story.
According to my interpretation, the landing point of the ark was understood to be the mountain called today Alo Dagh (37° 30' N, 44° 00' E), which is in the southern part of the area that used to be called Ararat. The original text of the Old Testament may have referred to this mountain by a specific name or simply as "the mountain of Ararat." The writers of the third hand had to face the problem that Alo Dagh is 4146 meters high, whereas according to them the level of the water after 150 days from the 17th of month II was 22,500 cubits = 9,988 meters. In order to patch up things, they went looking for the highest possible mountain in the area, which is the one which today is generally referred to as Mount Ararat (39° 47' N, 44° 46' E), the mountain called Agri Dagh according to modern Turkish official toponymy. This mountain, being a volcano, is higher than the general level of the mountains of the area, and reaches the height of 5165 or 5156 meters; the figures vary because the exact calculation of the height of a mountain is difficult to achieve even today. The writers of the third hand thought of bringing this mountain into the story; for this purpose they added the second part of verse 8:5. "The water receded until the tenth month; and the first day of the tenth month the tops of the mountains could be seen." This passage does not mean that the Ark grounded on the first day of month X, nor does it mean that the landing place of the Ark became visible on that day, but it does mean that mount Ararat became visible on that day. Since according to this version the Deluge began on the 17th day of month II, the waters would have reached their maximum height of 22,500 cubits on the 17th day of the 7th month, 150 days later. Therefore by "first day of the tenth month" the text means after 73 days of receding water. Since the water receded 150 cubits a day, on that day the level of the water was about 22,500 -- (73 x 150) cubits = 22,500 -- 10,950 cubits = 11,550 cubits = 5,127 meters.
The original version may have mentioned the specific landing place of the Ark, or may have referred to it by the phrase "the mountain of Ararat." But in any case, in the third version the phrase "the mountains of Ararat" is a deliberately vague expression which includes both the traditional landing place of the Ark, in the southern part of the geographical area called Ararat, and the mountain called Mount Ararat in later times, which is in the northern part of this area.