Internet of Mobile Things (IoMTs) refers to the interconnection of mobile devices, for example, mobile phones, vehicles, robots, etc. For mobile data, strong extra processing resources are normally required due to the limited physical resources of the mobile devices in IoMTs. Due to latency or bandwidth limitations, it may be infeasible to transfer a large amounts of mobile data to remote server for processing. Thus, distributed computing is one of the potential solutions to overcome these limitations. We consider the device mobility in IoMTs. Two situations of the movement position of the mobile devices, i.e., unpredictable and predictable, are considered. In addition, three possible relative positions between the two server sets which respectively correspond to the positions of a mobile device for computation tasks offloading and for output results receiving, i.e., within the same server sets, with two different server sets and with two adjacent server sets, are studied. Coded schemes with high flexibility and low complexity are proposed based on Fountain codes to reduce the total processing time and latency of the distributed fog computing process in IoMTs for the above different situations. The latency related performance, i.e., the computation, the communication and the transmission loads, is analyzed. We also compare of the Fountain code-based and the uncoded schemes and numerical results demonstrate that shorter total processing time and lower latency can be achieved by the Fountain code-based schemes.