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I was working on the following problem:

Two trains depart towards each other from $650\,\mathrm{km}$ apart. If they leave at the same time, they will meet after $10$ hours, but if one of them leaves $4$ hours and $20$ minutes after the other, they will meet $8$ hours after the second leaves. Determine the average speed of each train.

Since time and distance were already proportioned, I tabulated every $1,200$ seconds and used the URM velocity formula to get each train's velocity, but I got curious if there was a way to solve this problem with a numeric method, like for example the Gauss-Seidel, Dolittle, Crout or maybe Cholesky, instead of using the physics approach, maybe it would be a more precise result.

vitamin d
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Daniel
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    Well, $10x + 10y = 650$ and $8x + 12\frac 13 y = 650$ seems the most obvious strategy to me. – fleablood Jun 26 '21 at 23:47
  • Right! I was trying to do 650 - x, but clearly that's better – Daniel Jun 27 '21 at 00:43
  • I do love how this problem tries to get around assuming the trains travel at a constant speed by using "average speed" instead, but fails to realize that the two scenarios do not necessarily have the same average speeds, so the information given actually isn't sufficient for a solution. – Paul Sinclair Jun 27 '21 at 13:39

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