In this paper, we consider a relay assisted backscatter communication (RaBackCom) system, where a user backscatters incident signals from a carrier emitter (CE) to a relay and a receiver simultaneously, and then the relay forwards the user's information to the receiver for throughput improvement. We consider two cases that the relay is with/without an embedded energy source. Specifically, if the relay does not have an energy source, it first harvests energy from the signals from the CE and then uses its harvested energy for information forwarding. For both cases, we formulate time allocation problems on the user's information backscattering, the user's information forwarding, or the relay's energy harvesting to maximize the system throughput, and then derive closed-form solutions. Simulation results demonstrate the advantages of the proposed relay cooperation scheme with the optimal time allocation in terms of system throughput.