Would pushups combined with weightlifting make a good workout?
For general fitness, a one-hour workout with varied exercises is good. You could, for instance, do regular, wide, and diamond pushups, and mix your weight sets up. Whether it’s overtraining depends on your age. If you’re under 18 you may want to talk to a doctor before starting a serious strength training regimen to avoid bone and joint complications.
Depending on what weight exercise you are doing, there is nothing wrong with that. In fact, that is similar to P90X that you may have seen on TV – many of their workouts use your own bodies resistance for strength and toning. You want for the last several of each rep to be difficult, but you want to maintain good form. If you start getting sloppy, you’ve reached your max. If the last several are too easy, increase your weight. You will know if you are over training if you listen to what your body is telling you. Try not to over-do it right away and build up to your goals. Also, interspersing push up and pull ups in between weight training is a good form of muscle confusion and will help your overall workout (those moves will work your back, chest, shoulders and arms all together). Just make sure you include some cardio too.
