First simulations are presented for the dynamic spectra of a group of coronal type III bursts that are observed remotely at Earth. A three-dimensional model is developed, including the structure of the source region, dynamics of electron beams, Langmuir, ion-sound, and electromagnetic waves within the source, and propagation of radiation to Earth. For realistic coronal and beam acceleration parameters, the simulation results are consistent with the general characteristics of type III bursts. We demonstrate that multiple radio bursts at high frequencies in the group merge at low frequencies, due mainly to a previously proposed mechanism which leads to merging of beams in the presence of beams and Langmuir waves only. The radio flux after the merging, however, depends jointly on beam-wave and wave-wave interactions and propagation effects.