An effective medium approach together with a multiple scattering formalism is considered to study the steady-state dynamics of suspensions of spheres and polymer chains without excluded volume interactions. The polymer chains are assumed to obey rigid-body dynamics (without rotation) and are taken to be so long that Gaussian statistics is applicable. We have considered the dynamics of probe objects (either a sphere or a polymer) in a solution containing spheres and polymers. The significance of the dimensionless variables appearing when solving the effective medium equations and, in particular, the role of the geometrical parameter t = R(g)/a (a is the radius of any sphere and R(g) the radius of gyration of a polymer chain) are discussed. The translational diffusion coefficients of the moving probe sphere D-S and of the center-of-mass of the probe polymer chain D-P, and the shear viscosity of the suspensions have been derived. Both the friction coefficient of the probe sphere or that of the probe polymer chain and the shear viscosity diverge as Phi(POL)-->0.31 in the presence of polymers in the solution. Also, when polymers are diffusing in a suspension of fixed spheres an optimum range of Phi(SP) that maximizes the difference in the diffusion coefficients of polymer chains characterized by distinct t values has been noticed.