We prove that any polynomial-time $α(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(α(C))$-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where $C$ is the number of weakly connected components in the subgraph induced by the positive-demand arcs---a small number in many applications. In conjunction with known results, we obtain constant-factor approximations for $C\in O(\log n)$ and $O(\log C/\log\log C)$-approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial-time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on $C$ and since $C=1$ in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river.