What makes Xeno's paradox paradoxical? It sounds more like a trick question than a bona fide paradox. Achilles and the tortoise are going to have a half-mile race, and Achilles gives the tortoise a 1/4 mile head start. Suppose Achilles runs as fast as a decent male high school track athlete, and he can cover 1/2 mile in 2-1/2 minutes. He gives the tortoise a head start of 1/4 mile. According to a quick internet search, the average turtle moves at 3 to 4 mph. Let's say our tortoise is particularly fast, and moves at 5 mph. It thereby takes the tortoise 3 minutes to cover 1/4 mile. Achilles finishes 30 seconds ahead of the tortoise. Where's the paradox?

The reasoning you gave illustrates why Zeno's example has a chance of counting as a paradox at all. As you show, of course Achilles will overtake the tortoise. But Zeno claimed to have equally good reasoning showing that Achilles never overtakes the tortoise. That's the paradox: apparently good reasoning in favor of each of two incompatible claims.

For Zeno's reasoning and a critique thereof, see sections 3.1 and 3.2 of this SEP entry.

Read another response by Stephen Maitzen
Read another response about Space, Time