Most population models use either discrete time or continuous time. But what do we do in the case of a resource that grows continuously paired with a consumer that has a synchronized life history with annual birth pulses? Answer: We use a mixed time model consisting of differential equations on fixed time intervals and jump conditions. For analysis, it is better to think of it as a discrete model in which the continuous component is used to identify the discrete map. In this talk, I will show the simplest reasonable model for this scenario, and we will see that its dynamics can be even a little more complicated than a standard discrete model.