In as much as we need some rest during the period of exercise expecially push-up, going for 20 minutes rest is not a good idea I will still suggest you rest for 5 minutes though body system may not be thesame but am saying from experience. If you go for 20 minutes rest after your first reps you will notice your body will be weaker because it has taken enough rest that have lasted for 20minutes you won't able to do much push-up again in your next reps so I will suggest you go for a maximum of 5 minutes rest the body will still be active by then.