Achilles and the Tortoise

The tortoise challenged the great Greek warrior, Achilles to a race with an allowance of 100-metre head start. Although Achilles was such a strong and fast warrior, he would never be able to catch the tortoise, not to mention to overtake him.
In order for Achilles to overtake the tortoise, he had to run the 100 metres, bringing him to the tortoise's starting point. Since both Achilles and the tortoise were moving at the same time, by the time Achilles reached the tortoise's starting point, the tortoise should have moved forward some distance, say a metre. So the tortoise was a metre ahead of Achilles. In order to overtake the tortoise, Achilles then had to run that one metre, bringing him to the tortoise's new position. Again, since they both were moving at the same time, by the time Achilles reached the tortoise's new position, the tortoise should have moved forward yet some distance, albeit smaller this time. So the tortoise was still at some distance ahead of Achilles. Achilles then had to catch up with the new distance. But the tortoise yet moved forward another distance at the same time, albeit much smaller and smaller. So the tortoise was always at some distance ahead of Achilles, no matter how small it was. Therefore, Achilles would never catch the tortoise.
This is the famous Zeno's Paradox by the Greek philosopher, Zeno (490BC - 430BC). We know from common sense Achilles could overtake the tortoise in matter of seconds. But Zeno's argument was perfectly logical. How can we resolve this paradox?
I shall leave it to some later blog.