I am given to understand the generations denoted in the biblical texts are not necessarily contiguous but general ascriptions so that we know the texts have a sound basis in history. Hence the dating of the Tower of Babel is subject to uncertainty, as is your friend's programming in relation to potential re-population.
I don't know the individual who wrote that. However, I found it compelling. If you do not, then how about the other half of the equation? You said "let's do the math". Let's means "let us", meaning now it is your turn. Show mathematically how the earth could have been repopulated to its current level solely by the people on Noah's Ark, in the time allotted. "Doing the math" was your idea, after all.
The implications of this comment just struck me. Young Earth Creationism is based on the geneological dating of the bible, which puts the age of the earth at 6,000 years. Why are the generations of the bible good enough to accurately date the age of the entire universe, but not good enough to count the 180 years from the alleged flood to the alleged Tower of Babel?