This letter introduces a new model for backscatter assisted wireless powered communication networks (BAWPCNs) that include a hybrid access point (HAP) and multiple backscatter communication (BackCom) and traditional wireless powered communication network (WPCN) users. To make full use of time to transmit information, both backscatter and harvest-then-transmit (HTT) modes are employed. In the proposed model, during the first time slot dedicated for energy transfer in traditional WPCNs, the traditional WPCN users harvest energy radiated by the HAP, and simultaneously the BackCom users reflect modulated signals to the HAP. The traditional WPCN users are scheduled during the remaining time slots via time division multiple access (TMDA). The optimal time allocation policies for the half-duplex (HD) and full-duplex (FD) BAWPCNs are obtained to maximize the system throughput. The tradeoff between backscatter and HTT modes is analyzed. Simulation results demonstrate the superiority of the proposed model.