In this paper, we consider a wireless powered mobile edge computing (MEC) network, where the distributed energy-harvesting wireless devices (WDs) are powered by means of radio frequency (RF) wireless power transfer (WPT). In particular, the WDs follow a binary computation offloading policy, i.e., data set of a computing task has to be executed as a whole either locally or remotely at the MEC server via task offloading. We are interested in maximizing the (weighted) sum computation rate of all the WDs in the network by jointly optimizing the individual computing mode selection (i.e., local computing or offloading) and the system transmission time allocation (on WPT and task offloading). The major difficulty lies in the combinatorial nature of multi-user computing mode selection and its strong coupling with transmission time allocation. To tackle this problem, we propose a joint optimization method based on the ADMM (alternating direction method of multipliers) decomposition technique. Simulation results show that the proposed method can efficiently achieve near-optimal performance under various network setups, and significantly outperform the other representative benchmark methods considered. Besides, using both theoretical analysis and numerical study, we show that the proposed method enjoys low computational complexity against the increase of networks size.