  We derive two different sets of rate equations for sympathetic cooling of
harmonically trapped Bosons or Fermions. The rate equations are obtained from a
master equation derived earlier by Lewenstein et al. [Phys. Rev. A 51 (1995)
4617] by means of decoherence and ergodicity arguments. We show analytically
that the thermal equilibrium state is a stationary solution of our rate
equation. We present analytical results for the rate coefficients which are
needed to solve the rate equations, and we give approximate formulae that
permit their computation in practice. We solve the two sets of rate equations
numerically and compare the results. The cooling times obtained in both
approaches agree very well. The equilibration rates show fair agreement.
