The gas dynamic picture of a supersonic flow around the body having at the rear end the supersonic jet is presented. Reynolds number is assumed to be very large. The peculiarity of this flow conditions is the compound character of flow. The part of disturbed domain is occupied with a rarefied gas, another part is occupied with a dense gas. The problem is reduced to solving Boltzman equation for the rarefied gas and Navier - Stokes equations for the dense gas in the jet. The solutions of these equations are matched in the intermediate region. The estimates of main characteristics show that Navier - Stokes equations with slip conditions and the temperature drop on the solid surface may be used for the description of the flow around a body with the jet at altitudes until 250 km. Based on the results of numerical solutions, peculiarities of the physical picture of the flow are studied. The main peculiarity detected is the fact that the part of gas mass of the jet flows in the domain which is close to the side surface of the body.