1400’s and Endings

I hear it all the time from lower rated players: Study tactics. Endings and strategy should wait until you are (whatever) rating.  Well take a look at this ending played between a couple of 1400’s. White to move.

Play continued 51.Kb7 Kf2 52.Kb6 Ke2 53.Kb5 and Black resigned.  He should not have because the position is drawn. If you simply count moves from the starting position, in which it is obvious White must capture the P on a4, you will see it takes 4 moves (Kb7, Kb6, Kb4 and Kxa4).  Where will Black’s King be in 4 moves? …Kf2, …Ke3, …Kd4 and …Kc4 reaching this position:

When I showed this position to White he insisted that it was a win (and presumably so did Black) because all he had to do was play 55.Ka5 and meet …Kc5 with 56.a4 Kc6 with 57.Kb4 and he can advance the P and win.  This is not true. After 57...Kb7  58.Kb5 Ka7  59.a5 Kb7  60.a6+ Kb8  61.Kb6 Ka8  62.a4 Kb8  63.a5 Ka8 reaching the following position: 

And White either has to allow Black to capture his P’s or a stalemate.  Going back to the original position, it is a draw because White’s K can never get off the a-file without allowing Black to get in front of the P’s.  With a little elementary endgame knowledge both players would have known this and Black could have saved a half point.