In this study we propose to explain the discrepancy between classical models and the observational data of early type stars in eclipsing binaries by the existence of a rapidly rotating core in the primary, rather than by invoking a low metal abundance. Our claim is based on the analysis of the double lined eclipsing binary EK Cep, on which a strong constraint is put by its apsidal motion. We constructed models both with and without rotation for the components of the system. If the stars do not rotate, then, considering ( i) that both components have the same chemical composition and age, and (ii) that the primary star is exactly at the zero-age main-sequence point, we derive X = 0.614 and Z = 0.04 for respectively the hydrogen and heavy element abundances, with a mixing-length parameter alpha = 1.30, somewhat lower than that calibrated on the Sun. These values satisfy all the observational constraints at the single age of 26 Myr, except the luminosity and radius of the primary, and they are also in good agreement with the observed chemical evolution in the solar neighborhood. Since the observed luminosity and radius of EK Cep A are less than those predicted by a non-rotating model, we deduce that this star must have a rapidly rotating core, while its envelope is synchronized with the orbital motion due to tidal interaction. To achieve perfect agreement between the rotating model of this star and the observations, the requirement is that the central region rotates about 65 times faster than the synchronized envelope, which contains 48% of the star's total mass. We describe the effect of such differential rotation on the location of the star in the HR diagram, and compare it with that of rotation caused by contraction alone. We confirm also that such rapid rotation may account for the spread which is observed in the isochrones of open clusters.