Place cells and time cells in the hippocampus represent space and time, respectively, via a sparse code. However, a fraction of cells exhibit a mixed selectivity, firing at a specific time and place. This occurs even in tasks in which the animals position is completely independent of the elapsed time between relevant behavioral cues. This mixed behavior is yet to be explained by mathematical models. In this work, we trained a recurrent neural network that enforces competitive dynamics to simultaneously solve a path-integration task and to integrate time from presented stimuli. The model develops Place Cells, Time Cells, and the mixed code observed in experiments. We then simulated lesions between spatial tuning units and mixed units. This impairs the performance of both tasks, but the timing task’s performance can be partially recovered by training a new linear decoder. Finally, lesions to the model share behaviors with MEC-impaired animals, such as place cells becoming wider and noisier, and timing performance decreasing. Taken together, our results suggest that a competition mechanism could be responsible for the sparse code in the hippocampal formation and that a mixed representation of space and time could emerge even if these variables are not correlated in the environment.