I think doing body weight stuff and core is good, and you pretty well have to do some strength work when you get old. The ability to do pushups and having a strong core will help your form as you get tired in a race or workout. I do about a 10 min routine before I run and have for years. Seems to help loosen me up, and keeps me in tone. I do 20-25 pushups with half on the fingertips, and I'm 60.