Assuming that you have a TI-83/84...

HitMODE, then change "FUNC" to "PAR", and "SEQUENTIAL" to "SIMUL".

HitY=, and then enter in your equations.

HitWINDOW, then change the viewing dimensions to the following (these are my suggestions):

Xmin=0

Xmax=100

Xscl=10

Ymin=2

Ymax=4

Yscl=1

(I didn't mention the t-values; it's possible that you won't need to change them.)

Then hitGRAPH. Hopefully, you'll get a simulation.

I don't know if X1/Y1 wins the race or not, because on my calculator the graphs were rendered rather quickly. It might help if you figure out a set of parametric equations that will put a single, short line segment in the middle (at x = 50) to indicate the flag.

Don't forget to change the settings back inMODEwhen you're done.