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Assuming Person A, Person B and Person C trains chest and back the same day.

Person A performs 9 sets of chest first then proceeds to 9 sets of back.

Person B performs 9 sets of back first then proceeds to 9 sets of chest.

Person C perform 3 sets of chest, then 3 sets of back then 3 sets of chest and so on.

Further assuming that each of them weigh the same, have similar diet plans, train moderately heavy (8-12 Reps per set), have same goals of gaining equal amount of size on both the muscles and are training for building muscle mass;

Will Person A and Person B be training their second muscle less efficiently due to increased fatigue?

Will Person C be unnecessarily increasing his rest times for a particular muscle?

Which one of them will working out close to optimality for the accomplishment of the above-stated goal?

  • Are we considering all sets of a particular muscle group to be the exact same exercise? – JustSnilloc Mar 13 '18 at 2:29
  • Nope. 3 different exercises of 3 sets each. – Zaitorious Mar 13 '18 at 3:02
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There is idea of using antagonists, called super sets. That way you train - for instance - biceps and triceps in consecutive sets. When biceps is used, your triceps is relaxing. Triceps is not used, but also that is how our neural system works. That is one of Joe Weider's rules. Please look, for instance here.

Note that in your example that is not 100% super set - long head of triceps is used by both chest, and back exercises. Usually that limits this kind of "splits" for people with smaller experience. Not to mention that with arching during bench press - back is activated.

I see that you assumed that during chest set, back is resting. However overall load can influence that as well. Try to do additional jogging before chest day. Usually that means more energy burned, and your body needs some time to be prepared for that. Same goes with additional exercises. In long term, with plan - that can be good idea. But short term - you can see drop in performance. So there is not easy answer, or your question is a bit too broad.

Other point refers to size of the muscle. For bigger muscles, you can take much higher weights, but they also relax longer. So if I feel my chest burning, while triceps are not - I can do back exercise to relax chest, and balance stress during chest day. If that is not true, I can do biceps exercise. That goes a bit against previous paragraph, but - I'm writing about long term, and prefer to do something then to sit and wait, or watch my phone...

If you look for gain - plan is key. Muscles are growing during day or two after being stressed. If you train too much - large groups - like back, legs - needs, even 5 days to rest. So your muscles could get more impulses to grow, with limited soreness.

Hope it answers your question.

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