Much googling has not left me any the wiser, so here goes. Let FM be the distance between the mouths of two rivers X and Y. Let NS be the distance between the sources of the same two rivers X and Y. What pair of two rivers X and Y on Earth will produce the biggest quotient FM/NS? Or the smallest?

Two candidates for the biggest might be Indus and Brahmaputra but I am sure there are others.

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    Congo/Nile would be my first guess for a large quotient. Nile/Danube the smallest maybe? Could be solved rather easy in a GIS application. Data is available here. – Tactopoda Aug 9 '16 at 23:59
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    Re Much googling has not left me any the wiser, so here goes. Perhaps that's because this is a dubious metric. The Congo/Nile do not qualify because the sources of the Nile and the Congo are well removed from one another. The Yenesei/Amur is another option, but the sources (most distant from the mouth) of these rivers are hard to find in arid Mongolia. Other options are the Columbia and the Missouri/Mississippi, the Columbia and the MacKenzie, and the Amazon and the Colca. – David Hammen Aug 13 '16 at 23:03
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    @DH: TRUE source, like TRUE mouth, is an ill-defined concept for many, if not most big rivers, but we have to base our reasoning on something. However, I'm all ears as to how you would "de-dubiousify" this question. Obviously it somewhat tickled your brain cells because you gave a few counter examples which I am currently looking up. – tmsg Aug 14 '16 at 11:01
  • You need to add a lot of whys and wherefores to define 'source' and 'mouth' (and 'distance'!) for this problem before anything resembling an answer will emerge. And even then it will still only resemble an answer because different parameters will provide different answers, none of which means anything. – Spencer Aug 19 '16 at 2:07

Tbb is correct. The 'Congo and Nile' is by far the winner. Their mouths are 4600 km apart, whereas if you trek into the Rwenzori mountains, Western Uganda, there is s small highland swamp in a saddle point on the Congo-Uganda watershed. On either side there are several points where you can claim to be 'at the source', where you can stand with one foot in the Congo basin and the other foot in the Nile basin. The Indus and Brahmaputra are less than half this distance apart.

As for the other extreme, it's impossible to say. There are several rivers which end at more or less the same place. One then has to argue, 'Is one river a tributary of the other, or not?'

  • Thanks @Tbb and Gordon. I agree that it is hard to beat the Congo/Nile combo if you can literally stand with one foot here and the other there. Reminds me of an experiment I did many years ago on the equator. No one knew exactly where the line was but with a bucket of water and the Coriolis effect we could produce a pretty good estimate by measuring the distance between the points N and S where the water started to swirl and then halving that. The amazing thing was that it was just a few dozen metres between those points. I'd never have believed that this is enough to show the effect. – tmsg Aug 10 '16 at 13:43
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    ....And tmsg would have been right not to believe the draining bucket experiment!.A few metres from the equator the differential Coriolis force is so vanishingly small it is unmeasurable. In any case, it is billions of times weaker than the frictional irregularities of the draining bucket. At Nanyuki, Kenya there is a guy who 'proves' to tourists that he is on the equator by using two buckets whose drainage rotates in different directions, just 100 metres apart. It's a scam. If he exchanged the buckets he would get opposite results. – Gordon Stanger Aug 11 '16 at 23:53
  • Well... it was my own bucket, I filled it with water and I repeatedly tested, trying to keep external influences at a minimum. The effect was slight but reproducible. Perhaps the bucket was a "Clever Hans"? – tmsg Aug 12 '16 at 15:17
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    @tmsg -- There is no observable Coriolis effect in a typical bucket anywhere in the world, let alone near the equator where the Coriolis effect is essentially non-existent. One can see that effect far from the equator, but only with a very special bucket (a cylindrical bucket 2 meters across with a very small drain). Then one has to fill it carefully, cover it so as to keep air currents away, and let it settle for a day or two before opening the drain (Shapiro, "Bath-tub vortex," Nature 196 (1962): 1080-1081). – David Hammen Aug 13 '16 at 12:21
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    I totally disagree with David Hammem. There are numerous 'source's of both rivers, which can all be equally claimed. The Congo and Nile basins have a long common watershed. – Gordon Stanger Aug 13 '16 at 23:39

Geography seems especially prone to problems like this, where the use of seemingly simple terms results in a problem that is too vague to answer without arbitrary criteria defining them, and the arbitrariness of the criteria renders the so-called "answer" meaningless.

'Source' and 'mouth' are too ill-defined to allow an answer that means anything to emerge. (And what about distance? As the geodetic crow flies, or along the river's course?)

Any two rivers whose drainage basins border each other can considered to have a 'source' at the same point, meaning NS =0, and the quotient, as defined by the problem, is infinite, no matter how distant the two rivers' 'mouths'.

Even if we select some arbitrary point as the 'source' we have the case of the Casiquiare and the Orinoco. The Casiquiare flows out from the Orinoco into the Rio Negro, a tributary of the Amazon. The source of the Casiquiare is the source of the Orinoco no matter where you put it. So, infinity again.

If two rivers share a delta, such as the Ganges and Brahmaputra or the Amazon and Tocatins, they have the same 'mouths' as far as anyone can define so their FM must be 0. But in that case their drainage basins border each other, so FM/NS = 0/0, which is the true answer,

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