2012 AMC 10A Problem 16

Let us find the amount of time that it takes for the runner running at $4.8$ meters per second to lap the slowest person. We must have that $$4.8x - 4.4x = 500$$$$x = 1250,$$ where $x$ is the amount of time it takes for the faster runner to lap the other. Note that $4.4 \cdot 1250 = 5500,$ which means that these two runners always intersect at the starting line. We now have to find the least time, $t,$ such that $t$ is a multiple of $1250$ and the fastest runner ends up at the starting line. Every $1250$ seconds, the fastest runner runs $1250 \cdot 5 = 6250$ meters. Then in $2500$ seconds, the fastest runner runs $12500$ meters, which is a whole number of laps. Thus, C is the correct answer.