  We answer a question of Gy\'arf\'as and S\'ark\"ozy from 2013 by showing that
every 2-edge-coloured complete 3-uniform hypergraph can be partitioned into two
monochromatic tight paths of different colours. We also give a lower bound for
the number of tight paths needed to partition any 2-edge-coloured complete
r-partite r-uniform hypergraph. Finally, we show that any 2-edge-coloured
complete bipartite graph has a partition into a monochromatic cycle and a
monochromatic path, of different colours, unless the colouring is a split
colouring.
