Rorqual whales (Balaenopteridae) obtain their food by lunge feeding, a dynamic process that involves the intermittent engulfment and filtering of large amounts of water and prey. During a lunge, whales accelerate to high speed and open their mouth wide, thereby exposing a highly distensible buccal cavity to the flow and facilitating its inflation. Unsteady hydrodynamic models suggest that the muscles associated with the ventral groove blubber undergo eccentric contraction in order to stiffen and control the inflation of the buccal cavity; in doing so the engulfed water mass is accelerated forward as the whale's body slows down. Although the basic mechanics of lunge feeding are relatively well known, the scaling of this process remains poorly understood, particularly with regards to its duration (from mouth opening to closure). Here we formulate a new theory of engulfment time which integrates prey escape behavior with the mechanics of the whale's body, including lunge speed and acceleration, gape angle dynamics, and the controlled inflation of the buccal cavity. Given that the complex interaction between these factors must be highly coordinated in order to maximize engulfment volume, the proposed formulation rests on the scenario of Synchronized Engulfment, whereby the filling of the cavity (posterior to the temporomandibular joint) coincides with the moment of maximum gape. When formulated specifically for large rorquals feeding on krill, our analysis predicts that engulfment time increases with body size, but in amounts dictated by the specifics of krill escape and avoidance kinematics. The predictions generated by the model are corroborated by limited empirical data on a species-specific basis, particularly for humpback and blue whales chasing krill. A sensitivity analysis applied to all possible sized fin whales also suggests that engulfment duration and lunge speed will increase intra-specifically with body size under a wide range of predator-prey scenarios. This study provides the theoretical framework required to estimate the scaling of the mass-specific drag being generated during engulfment, as well as the energy expenditures incurred.