The Tower of Bavel/Babel was at the end of Peleg's life not the Beginning

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In Breishit/Genesis 10:25 it says:
And to Eiver{Eber} were born two sons; the name of the one, Peleg, for in his days was the earth divided and the name of his brother, Yoktan {Joktan}.
Rashi comments concerning this verse: The languages were confused and they were spread abroad from the plain and were separated throughout the entire world.
We learn (from this verse) that Eiver{Eber} was a prophet since he called the name of his son after a future event.
And we learned in Seder Olam that at the end of his {Peleg's days} they were separated; for if you contend that they were separated at the beginning of his days, (you will discover) that is not true; for Yoktan his brother was younger { than Peleg} and yet he
begot many families prior to this (division at the tower of Bavel/Babel).
For it was stated (Breishit/Genesis 10:26) "And Yoktan begot", etc.; and afterwards (the account of the division at the Tower of Bavel/Babel, which starts with the words in chapter 11) "And the whole Earth was", etc.
Now if you will contend that it took place in the middle of his days, scripture does not come to conceal, rather to clarify; therefore you must deduce that in the year of the death of Peleg, they were divided.