An "independent-quark model" for mesons and baryons which recently was applied very successfully to elastic scattering at high energies, is extended to inelastic meson-baryon and baryon-baryon reactions. A number of relations between cross sections are derived, most of which are independent of $\mathrm{SU}(3)$. The agreement with the available data is fair except for one case, but more data at higher energies are needed for a detailed test of the model.