In this paper, using the compatible theory of differential invariants, a
class of exact solutions is obtained for nonhomogeneous quasilinear
hyperbolic system of partial differential equations (PDEs) describing
rate type materials; these solutions exhibit genuine nonlinearity that
leads to the formation of discontinuities such as shocks and rarefaction
waves. For certain nonconstant and smooth initial data, the solution to
the Riemann problem is presented providing a complete characterisation
of the solutions.