Many cellular components are transported using a combination of the actin- and microtubule-based transport systems. However, how these two systems work together to allow well-regulated transport is not clearly understood. We investigate this question in the Xenopus melanophore model system, where three motors, kinesin II, cytoplasmic dynein, and myosin V, drive aggregation or dispersion of pigment organelles called melanosomes. During dispersion, myosin V functions as a "molecular ratchet" to increase outward transport by selectively terminating dynein-driven minus end runs. We show that there is a continual tug-of-war between the actin and microtubule transport systems, but the microtubule motors kinesin II and dynein are likely coordinated. Finally, we find that the transition from dispersion to aggregation increases dynein-mediated motion, decreases myosin V--mediated motion, and does not change kinesin II--dependent motion. Down-regulation of myosin V contributes to aggregation by impairing its ability to effectively compete with movement along microtubules.