No, calculus does in fact resolve them. More specifically, formalizing continuity and completeness obviates the issue. Like I said, if you distinguish between countable and uncountable infinities, there is no longer a paradox.

The only reason it appears to be paradoxical is because you're mandating someone move from a real coordinate (a, b, c) to another real coordinate (a', b', c') on the interval [x, y] while also passing through the set of all real points between them, without first defining a notion of distance of time. That's not possible for the same reason you can't ask someone to count all reals on an interval, because continuity implies uncountability. Between any pair of real numbers is another real number, and it takes an equal amount of effort (and time) to count any given number.

To a first glance, this seems like a paradox because we can clearly move from (a, b, c) to (a', b', c), yet we shouldn't be capable of any movement whatsoever. Calculus solves this problem by formalizing Zeno's demand as a geometric series with a notion of distance. The requirement is that you move from one position to another position while passing through every halfway position between them. Equip the vector space ℝ^3 with the Euclidean metric so you have a metric space (defined distance). Then we have the sequence of steps

    (a, b, c) -> |(a, b, c) - (a', b', c')|/2 -> ... -> (a', b', c')

which corresponds to the geometric series

    (1/2)^1 + (1/2)^2 + (1/2)^3 + ...

that series converges to 1: https://www.wolframalpha.com/input/?i=(1%2F2)%5E1+%2B+(1%2F2....

More concretely: an infinite expansion such as 0.99999999... is equal to 1. Each half step will take only half as long to traverse as the half step preceding it to it once you've defined Euclidean distance on a continuous space. The first step to formalizing sequences and series like this is by constructing the real numbers as a continuous set and distinguishing between different types of infinities. Then you can define limits, and from there you're essentially done.

Note that at no point am I talking about what happens when you reach 1, or (a', b', c'), or anywhere else. I'm just explaining how you reach it in finite time. If you can get arbitrarily close to a point, you can get to the point itself.

I guess I should be more technical and say that real analysis solves this problem, because what's really doing the heavy lifting here is the topology induced by defining a metric on ℝ^3 in combination with the notion of limits.