We consider the achievable average rates of a multiple-access system, which consists of N energy-harvesting users (EHUs) that transmit information over a block fading multiple-access channel (MAC) and a base station (BS) that broadcasts radio frequency (RF) energy to the EHUs for wireless power transfer. The information (over the uplink) and power (over the downlink) can be transmitted either in time division duplex or frequency division duplex. For the case when the EHUs battery capacities and the number of transmission slots are both infinite, we determine the optimal power allocation for the BS and the optimal rates and power allocations for the EHUs that maximize the achievable rate region of the MAC. The resulting online solution is asymptotically optimal, and also applicable for a finite number of transmission slots and finite battery capacities.