  We show an averaging result for a system of stochastic evolution equations of
parabolic type with slow and fast time scales. We derive explicit bounds for
the approximation error with respect to the small parameter defining the fast
time scale. We prove that the slow component of the solution of the system
converges towards the solution of the averaged equation with an order of
convergence is 1/2 in a strong sense - approximation of trajectories - and 1 in
a weak sense - approximation of laws. These orders turn out to be the same as
for the SDE case.
