But then, different passages in the Wikipedia article contradict each other (first section: 39-K is converted into 39-Ar by neutron bombardment; but "age equation" section: 40-K is bombarded; I think it should be 39-Ar).
There's a more basic explanation here: books.google.com/…
The Washington Post article Scientists discover hundreds of footprints left at the dawn of modern humanity describes the geological dating of stratified layers of mud by analyzing and dating minerals within each layer.
But since floods jumble materials of different origins and ages together, that meant the scientists had to date dozens of different minerals.
Instead of measuring 40K/40Ar, you assume a fixed 39K/40K ratio, convert a fraction $f$ of 39K to 39Ar by (n,p), then measure 39Ar/40Ar.