Not too sure cause I don't swim competitively. But I do know that both swimming and running involve have good cardio. So yes running will improve your swimming and im guessing yes also that swimming will help your running as in long distance wise having stamina.
Yes, logically it should, and I'm sure that it will if you swim and run for recreation/fitness. Oddly though, higher-level competitive swimmers tend to make horrible runners (not that they can't, they just tend to be slow), and I have no clue why. I've only ever known one girl that was a pretty good competitive swimmer and a excellent runner, and she had to give up swimming anyways for collegiate running.
Possibly its the muscle groups that swimming uses that aren't necessarily built up by running, and the shoulders and upper-body that swimmers get don't work well for running...
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