When engaging in concurrent multitasking, it quickly becomes clear that some activities combine well, while others do not. But which factors determine the compatibility of different tasks? We propose that the overlap in cognitive resources causes interference between tasks that limit performance, and that this performance can be predicted using a cognitive model. To test this, we built a model of three tasks, each using a well-defined set of cognitive resources. These tasks were executed separately as well as concurrently and the performance of the model was recorded. Afterwards, we ran an experiment where participants had to perform the same paradigm. Our results show that the model prediction has a good qualitative fit to the participant data: task combinations with more resource overlap had lower performance when performed concurrently, compared to combinations with little or no overlap.