You would run a 2-Sample T-Test. On your TI-83, input the values for the Before/After into a list. Do you know how to do that:

STAT>>EDIT, and then input Before in L1, and after in L2.

You then run your 2-Sample T-Test with population mean for L1 greater than population mean for L2, as you are trying to demonstrate that the times for these runners after their training is LESS THAN the times for the runner before their training.