The rate- and temperature-dependent plastic flow in a material containing two types of thermally activatable obstacles to dislocation motion is studied both numerically and theoretically in a regime of relative obstacle densities for which the zero-temperature stress is additive. The numerical methods consider the low-density 'forest' obstacles first as point obstacles and then as extended obstacles having a finite interaction length with the dislocation, while the high-density 'solute' obstacles are treated as point obstacles. Results show that the finite-temperature flow stresses due to different obstacle strengthening mechanisms are additive, as proposed by Kocks et al, only when all strengthening obstacles can be approximated as point-like obstacles. When the activation distance of the low-density extended obstacles exceeds the spacing between the high-density obstacles, the finite-temperature flow stress is non-additive and the effective activation energy differs from that of the Kocks et al model. An analytical model for the activation energy versus flow stress is proposed, based on analysis of the simulation results, to account for the effect of the finite interaction length. In this model, for high forest activation energies, the point-pinning solute obstacles provide a temperature-dependent backstress sigma(b) on dislocation and the overall activation energy is otherwise controlled by the forest activation energy. The model predictions agree well with numerical results for a wide range of obstacle properties, clearly showing the effect due to the finite interaction between dislocation and the obstacles. The implications of our results on the activation volume are discussed with respect to experimental results on solute-strengthened fcc alloys.