Is this the correct tale of the story of the tortoise and the hare, or am I mistaking it for another one?

A tortoise and a hare are having a race. When the hare arrives, the tortoise is already there. so the hare demands a rematch, racing back to the starting point, where the tortoise already awaits. they do that many times, until the hare dies from exhaustion. It turns out, there were tortoise twins, with one of the twins waiting at each end. They were conspiring to kill the hare.