Mathematical modeling of kinetic processes with different time scales allows a reduction of the governing equations on the basis of quasi-steady-state approximations (QSSA). Below the QSSA theorem is applied to a modified mathematical model of the microRNA repression on the protein translation with participation of eIF4F translation initiation factors. In accordance with the terminology of the QSSA theorem two of the protein concentrations are denoted as 'fast varying', such that the corresponding kinetic equations form a system attached to the system for 'slow' variables that consists of equations for the other four concentrations. We obtain analytic solutions related to the steady-state values of the fast varying concentrations and the slow varying ones, and the interpretation of these solutions are as restrictions on the regulatory role of microRNAs on the protein translation process.