"We move away from this river."
Translation:Elköltözünk ettől a folyótól.
Logically, maybe, but "halad" is not really used in this sense. It is used mostly to describe a continuous movement, in progress. As in being on its way. For example, the new space probe is moving towards Mars. "A Mars felé halad." On its way it passes by Jupiter. "Elhalad a Jupiter mellett."
Here, I would say "eltávolodunk", literally, "distancing ourselves (away)". Or just "elmegyünk", we go away.
The space probe is also moving away from (putting some distance between itself and) Saturn. "(El)távolodik a Szaturnusztól."