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Zeno's ancient paradox depicts a race between swift Achilles and a slowtortoise with a head start. Zeno argued that Achilles could never overtake thetortoise, as at each step Achilles arrived at the tortoise's former position,the tortoise had already moved ahead. Though Zeno's premise is valid, hisconclusion that Achilles can "never" pass the tortoise relies on equatinginfinite steps with an infinite amount of time. By modeling the sequence ofevents in terms of a converging geometric series, this paper shows that such aninfinite number of events sum up to a finite distance traversed in finite time.The paradox stems from confusion between an infinite number of events, whichcan happen in a finite time interval, and an infinite amount of time. Thefallacy is clarified by recognizing that the infinite number of events can becrammed into a finite time interval. At a given speed difference after a finiteamount of time, Achilles will have completed the infinite series of gaps at the"catch-up time" and passed the tortoise. Hence this paradox of Achilles and thetortoise can be resolved by simply adding "before the catch-up time" to theconcluding statement of "Achilles would never overtake the tortoise".

The Fallacy in the Paradox of Achilles and the Tortoise