First of all, sorry for my English, because I am from Russia. The task is:
We are given two points (see image) - $(x_1, y_1)$ and $(x_2, y_2)$. Point $(x_2, y_2)$ is moving and has a speed of $V_{x,1}$ on the X axis and $V_{y,1}$ on Y axis. Point $(x_1, y_1)$ is not moving yet, but can move and if it does, has a speed of $V_{x,2}$ on X axis and $V_{y,2}$ on Y axis. Knowing all the variables listed above, except for $V_{x,2}$ and $V_{y,2}$ (as for them we know only that $\sqrt{V_{x,2}^2 + V_{y,2}^2} = S$), find the point $(x_3, y_3)$, in which points $(x_1, y_1)$ and $(x_2, y_2)$ will meet, if the point $(x_1, y_1)$ starts moving right now.
I am using it in my computer program and i've already came up with almost working solution - but this solution is simple run over all possible positions in a loop and it is very inefficient.
Assuming that $(x_1,y_1)$ is capable of infinite acceleration (it's not as if points had mass), you need to solve
$(x_3,y_3)=(x_1,y_1)+(v_{x2},v_{y2})t=(x_2,y_2)+(v_{x1},v_{y1})t$