In edge-cloud computing, a set of servers are deployed near mobile devices to allow these devices to offload theirjobs to the edge servers with low latency. One fundamental problem in edge-cloud systems is how to dispatch and schedule the jobs so that the job response time (defined as the interval between the release of the job and the arrival of the computation result at its device) is minimized. In this paper, we propose a general model for this problem, where the jobs are generated in arbitrary order and times at mobile devices and offloaded to servers with both upload and download delays. Our goal is to minimize the total weighted response time of all the jobs. The weight is set based on how latency sensitive the job is. We derive the first online job dispatching and scheduling algorithm in edge-clouds, called OnDisc, which is scalable in the speed augmentation model; that is, OnDisc is (1 + ϵ)-speed O(1/ϵ)-competitive for any small constant ϵ > 0. Moreover, OnDisc can be easily implemented in distributed systems. Extensive simulations based on a real-world data-trace from Google show that OnDisc can reduce the total weighted response time dramatically compared with heuristic algorithms.