The purpose of this paper is to develop a fast heuristic called FastCARP for the solution of very large-scale capacitated arc routing problems, with or without duration constraints. This study is motivated by a waste collection problem in Denmark. After a preprocessing phase, FastCARP creates a giant tour, partitions the graph into districts, and construct routes within each district. It then iteratively merges and splits adjacent districts and reoptimises the routes. The heuristic was tested on 264 benchmark instances containing up to 11,640 nodes, 12,675 edges, 8,581 required edges, and 323 vehicles. FastCARP was compared with an alternative heuristic called BASE. On small graphs, it was better but slower than BASE. On larger graphs, it was much faster and only slightly worse than BASE in terms of solution quality.