Conventional theory used to be work out one day, rest the next and so on.
I never subscribed to that. When I was working out, I'd hit it every day and work hard. Usually the same exercises but not always. I'd thrown in a light weight day, or a dumbell day or only cable day, just to get some variety. Not saying your gym rat friend is wrong, but once a week? I don't know how you make progress like that.
I assume you are doing other exercises? That's important. I always did my large muscle group exercise, like bench presses, first and then the smaller muscle groups like arms, at the end. IIRC, I did bench presses, upright rows, cable pull downs, some cable shoulder work, then bicep and triceps work. I always tried to alternate opposing muscle groups and I worked pretty quick. The easiest to understand is the arm work. I'd do a set of bicep curls and then get over to the triceps machine and do a set there, then back to biceps and so on. Five sets for everything.
If you are doing other work, I'd suggest concentrating on bench presses. That will help your push ups because you can get a lot more resistance, and hence strength, with a bench press.
And remember, what works for one person doesn't necessarily work for another. If you're a power lifter, odds are you're kind of squat and short. Very strong, but a tall thin guy is not likely to be a power lifter.
Good luck!
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Pat Tillman (1976-2004):
4 years Arizona State University, graduated with high honors.
5 seasons National Football League player, Arizona Cardinals.
Forever United States Army Ranger.