¿Can you believe in an old earth and a global flood?

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I ve noticed that most pages that defend a global flood also defend a young earth.

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Part of the reason for this is that a global flood is the way in which many YECs choose to dismiss geological evidence for the age of the earth. There's an awful lot of sedimentary rock in the world to squeeze into a 6000 year history, and saying "most of it must be from the flood" provides a mechanism for it to get there. It can then be argued from there that the order in which species occur in the rocks are due to hydraulic sorting of their remains rather than the order in which they lived. Neither of these survive close scrutiny.
Take away the flood, and it's back to the drawing board.

I don't know the river you're talking about, so I can't deal in specifics here, but here's one possible explanation. Maybe the river system predates the mountains. If a pre-existing river can downcut faster than a mountain range can rise, it will carry on through.Another explanation is headwater erosion and stream capture. At the top, there's a plain with a river system flowing west. South of that is a mountain range, and south of the mountains is a plain lower than the northernmost one. A river developed on the mountains and cut a valley backwards until it reached the northern plain. Eventually it breaches the channel of the northern river, which then follows the new path of least resistance southwards, leaving part of it's old course dry.I don't really see what's illogical about this.
What's your explanation then?