Wasn't this avoiding the answer ? o.oKakashi was a jounin and Rin was a chunin by this point, and it wasn't long after this that Minato became Hokage, so I think they eventually disbanded as a formal team.
After Rin's death, Minato was already Hokage??? (Possibly) and Kakashi was probably in Anbu? I forget the age he was in Anbu.