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Try mixing in some cycling with your running—maybe three days of running and three days of riding each week, then take one day off.
Of course, the pace and distance depend entirely on how fit you feel, so don't push too hard. Just listen to your body and take breaks whenever you need them. Eventually, you'll find you can go faster and longer without feeling wiped out.
Hill training is great, but I'd stick to flat ground for a while when you're just starting out.