You can easily walk 10 miles
Build leg strength as you work out for a 10 mile run
Keep walking. Your legs have the strength they need to run. What you need to develop is muscle endurance. Squats will build strength, but they won't give you the stamina. You should give your muscles some rest even after 6 km, if they really tire your legs that much.
Alternating days when your legs feel tired, exhausted, or "devastated" with days when you can either lightly jog or rest. That way, you can go a little further on some runs and adjust your muscles after those runs. Eventually, you should find that you were able to build enough stamina to run the entire 10 miles.
Try to break your runs down into:
3-4k easy - that shouldn't make your legs tired - think "recovery jog"
It's a little more distance than weekly, but the recovery jogs and rest days break up your longer runs so it should either feel similar or easier. As a result, your legs should feel a little fresher on the 6k and 8k runs. After a week, check to see if you can turn your 6K runs into 7K or 8K runs and your 8K runs into 9K or 10K runs. Once you are comfortable with this, try doing 5k easy instead of 4k easy the following week. If your legs feel slightly tired after 5 km, return to 4 km. Always add a bit of space to the start of your 6K and 8K runs, but keep your rest days relatively short and simple.
Notes on stimulation:
- Recovery jogs / easy runs should feel easy. You should be able to have a conversation throughout the run, and it shouldn't make your muscles feel any more tired than they did before the run.
- Your longer days may be a bit faster, but since your current goal is endurance, you should try to maintain the same steady pace throughout the run.
- Go by feeling, not time. You can worry about pace / km, training, and race times after you have the stamina to run the full 10 miles with relative ease.
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