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.