I did a similar 10-day trek in Peru. I'm assuming you'll land in cuzco. I would spend a few days in cuzco before the trek. That should help tremendously. Rest! It'll be tough on your body, so make sure you get plenty of sleep to recover. Drink lots, avoid caffeine. Something that works wonders in Peru is coca leaves. Hotels will have them available for free for people. It is highly recommended that you chew some, it is very helpful in overcoming altitude issues. People also have coca tea, although that doesn't work as well. There is some special mountain mint tea that is supposed to help too. Ahead of time, you can do a lot cardio, just to get your overall cardiovascular fitness up. Basically the fitter you are in that area, the quicker you can adapt to the altitude. Something I recommend, if it's possible in your area, is stairs running. Literally run up and down stairs. I remember there was a competition in the local ball field where I used to live. It's not as uncommon as you might think, so look it up, you might find some people to do it with you. This isn't strictly altitude related, but something that was interesting during my trek is my wife, who swims a lot, hikes and backpacks frequently had a hard time with her knees, because the trails there can get very steep, much steeper than our local trails were at the time. Whereas, I, being a runner, had a much easier time. Somehow, my knees must be better conditioned being a runner. She trained on the stair masters before we went, but going down is what killed her. She had never trained going in that direction.
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