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The radio galaxy 3C 75 is remarkable because it contains a pair of radio-loud active galaxies, each of which produces a two-sided jet, with the jet beams appearing to collide and merge to the west of the galaxies. Motivated by 3C 75, we have conducted three-dimensional hydrodynamic simulations of jet collisions. We have extended previous studies by modelling the physical properties of the cluster atmosphere, including an external wind, and using realistic jet powers obtained from observational data. We are able to produce a morphology similar to that of 3C 75. The simulations imply that direct contact between the bulk jet flows on the west of the source is required to produce a morphology consistent with 3C 75. We quantify how the merging jets decelerate, how the wind deflects the jets and cocoons, the entrainment of intra-cluster material into the cocoons, the cocoon energetics, and how the jet interactions generate enstrophy. By comparing simulations of pairs of two-sided jets with those of single two-sided sources, we determine how the interaction between two bipolar jets changes their evolution. The unprecedented sensitivity and angular resolution of upcoming observatories will lead to the detection of many more complex sources at high redshift, where interacting jets are expected to be more numerous. The morphology of these complex sources can provide significant insight into the conditions in their environments.