Each of two runners at either end of a 1907 m straight track jogs toward the other at a constant 4.00 m/s. Suppose that a fly were to go back and forth, essentially without a pause, from one runner to the other at an average speed of 13 m/s. How far will it have traveled in total by the time the athletes meet?

Multiply the fly's speed (13 m/s) by the time it takes the runners to meet (1907/8 = 238.4 s. I get 3099 m.

Are you sure the figure 1907 m is correct? It seems an odd length for a straight track. It looks like a typo.