The answer varies by the river. In the extreme case of the Amazon, by far the largest river in the world, you can be at sea, out of sight of land, and still the water is fresh enough to drink. Most rivers are undrinkably salty well before they reach their mouth, especially as rivers tend to flow more slowly nearer the coast and tides can push sea water many miles inland. Faster flowing rivers in areas of small tides can have fresh water close to their mouths.
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