I can't remember off the top of my head, but I think combat medics are like 60 weeks of training/school. Army basic training is  between like ten to fifteen weeks depending on the job. 

If I remember right, Nate would be in training for about a year and half. So he'd be 19 or 20 before ever seeing any real combat. So you'd figure what? Four  or five year of combat? It makes sense to me.