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Mobile edge computing (MEC) is one of the promising solutions to process computational-intensive tasks for the emerging time-critical Internet-of-Things (IoT) use cases, e.g., virtual reality (VR), augmented reality (AR), autonomous vehicle. The latency can be reduced further, when a task is partitioned and computed by multiple edge servers' (ESs) collaboration. However, the state-of-the-art work studies the MEC-enabled offloading based on a static framework, which partitions tasks at either the local user equipment (UE) or the primary ES. The dynamic selection between the two offloading schemes has not been well studied yet. In this paper, we investigate a dynamic offloading framework in a multi-user scenario. Each UE can decide who partitions a task according to the network status, e.g., channel quality and allocated computation resource. Based on the framework, we model the latency to complete a task, and formulate an optimization problem to minimize the average latency among UEs. The problem is solved by jointly optimizing task partitioning and the allocation of the communication and computation resources. The numerical results show that, compared with the static offloading schemes, the proposed algorithm achieves the lower latency in all tested scenarios. Moreover, both mathematical derivation and simulation illustrate that the wireless channel quality difference between a UE and different ESs can be used as an important criterion to determine the right scheme.