Experts are split on this issue. The majority of fitness experts will advise you to do the cardio after the weight training, because if you do cardio first, it uses up much of the energy source for your anaerobic work
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This same view holds that strength training first will deplete the muscles' stored carbohydrates (glycogen or sugar), and therefore, it will enhance fat burning during the cardio workout
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If your primary goal is to increase your aerobic endurance or lose body fat, then you should perform cardio first.
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If your primary goal is to increase muscular strength, then do strength training first.
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To get the most out of your workout, perform the exercise that is most important to your goals first, when you are not fatigued.
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If your fitness goals include overall improvements, finish your workout with the type of exercise you enjoy most.
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I see a lot of people who have set a goal of losing fat around their midsection, and they spend an hour on the bench press or doing tons of curls
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The problem is that when they are done, they are too fatigued or don't have time to have a quality cardio workout.
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Lifting weights does not equal "big" automatically, and you won't firm those muscles on the treadmill.
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Spend 10 minutes at the beginning of your workout working on your legs, chest, back, shoulders and arms and then go for your stair-stepping marathon. You will be shocked at how much more toned you become.