A detailed comparison is made of the speed-time profiles of solar wind streams observed between June 1 and October 1, 1973, by instruments aboard Imp 7 at 1.0 AU and Pioneer 10 at 4.5 AU. This period includes a short interval when Pioneer 10 was coaligned with Imp 7 and the sun. The comparison provides several vivid illustrations of the phenomena of stream steepening in the solar wind with the attendant formation of forward-reverse shock pairs and the gradual decay of stream amplitudes with increasing heliocentric distance. In some respects the interplanetary medium appears to act like a 'low-pass filter'; large-amplitude short-wavelength speed structures present at 1 AU are generally subdued or absent at 4.5 AU. A simple fluid model of stream propagation which neglects all dissipation effects except those occurring at shock interfaces is employed to predict quantitatively the radial evolution of the stream structure observed at 1 AU. In most cases the model provides an adequate description of the large-scale features of the stream structure observed near 4.5 AU by Pioneer 10, including the amplitude of the speed fluctuations, the presence of abrupt jumps in speed at the leading edges of streams, the time of arrival at 4.5 AU, the filtering out of short-wavelength structures, and the overall shape of speed-time profiles. The model does less well in predicting the detailed structure at the leading edges of streams, e.g., the amplitude of the abrupt speed jumps. In the case of coalignment of Pioneer 10 with Imp 7 and the sun this lack of detailed agreement undoubtedly arises from the model's assumption of adiabatic flow (except at shocks) and its neglect of magnetic forces and nonradial flow. For other times, the above reasons plus the nonstationary nature of solar wind streams contribute to the lack of detailed agreement.