Solar energetic particle (SEP) events are well-associated with solar flares. It is observed that the delay between the time of the flare and the first-arriving particles at a spacecraft increases with increasing difference between the flare longitude and the foot point of the field line on which the spacecraft is located. This difference we call the connection angle and can be as large as ~120¿. Recently it has been found that all SEP events are preceded by type III radio bursts. These bursts are plasma emission caused by the propagation of 2--50 keV flare electrons through the solar corona and into the solar wind. The drift of these type III radio bursts to lower and lower frequencies enables the propagation of the flare electrons to be traced from the Sun to about 1 AU. We have made an extensive analysis of the type III bursts associated with >20 MeV proton events and find that, in most cases, the radio emission extends to the local plasma frequency when the energetic particles arrive within a few hours of the flare. We conclude that this emission at the lowest possible frequency is generated close to the spacecraft. We then use the time from when the burst started at the Sun to when it reached the local plasma frequency to infer the time it took the radio producing electrons to travel to the spacecraft. We find that these delay times are organized by the connection angle and correlate with the proton delay times. We also find that the differences between the radio delays at Wind and Ulysses are matched by differences in the relative arrival times of the energetic particles at the two spacecraft. The consistent timing between the relative arrival times of energetic electrons and protons and the start of the lowest frequency radio emissions suggests that the first arriving particles of both species are accelerated as part of the flare process and that they propagate to the spacecraft along trajectories similar to those of the lower-energy flare electrons. To be detected by observers at locations distant from the nominal field lines originating in the flaring regions the particles must undergo lateral transport. The continuity of the radio bursts suggests that the cross-field transport occurs in the interplanetary medium.