In this paper, the dynamics of solids mixing in a fluidized bed with horizontal tubes subjected to impulse and pulse input of tracer is simulated using the 'Cinematic' model. The dynamic mass balances are also solved using Laplace transforms followed by numerical inversion and a time-domain comparison is presented from the time of injection of the tracer until the steady is attained. It is demonstrated that due to the presence of sharp wave fronts, the numerical inversion procedure does not result in complete and accurate solutions. In general, the inversion is very slow and the accuracy of the results is restricted to a maximum of three significant digits. The numerical inversion required the computations to be performed individually for the three phases while the 'Cinematic' model calculates complete profiles in one sweep. In most trials, the numerical inversion procedure required a large number of terms to achieve convergence. Also, performing an important check such as the conservation of the tracer solids in the bed proved to be a very tedious task with Laplace transforms while the 'Cinematic' model did not demand additional efforts in performing the same check. Since many countercurrent systems can be represented by a system of hyperbolic partial differential equations similar to the one presented in this paper, the method of solution given in this paper can be regarded as applicable to other countercurrent systems as well.