Training other parts of the body to be stronger will not only help you become a faster runner, improving your chances of reaching your goals, but will also help prevent injury...again improving your chances of reaching your goals. Did you spot the common thread? Exercises such as squats, lunges, planks, leg raises, russian twists, pressups and others will strengthen not only the muscles required for running, but also other less obvious muscles, in your core such as the abs, neck and back which in turn will help you maintain better running posture. This is how it benefits you as a runner. When you look at a lot of runners taking on a hard run, be it fast or long, the thing that goes first is the posture. The body simply tires and starts to fold a bit as it struggles to hold onto good posture. When you adopt this 'tired runner' posture you hugely increase the chance of injury. 

There is a great article on runners world here, with examples of the sorts of exercises mentioned above and another great set of exercises here.

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