The van der Waals equation of state is used for correlation (using a single binary interaction parameter) and prediction of liquid-liquid equilibrium in many mixtures including a solvent and a polymer. The equation of state parameters for the polymer are estimated from experimental volumetric data at low pressures. For the solvent, the equation of state parameters are estimated via the classical method, i.e. using the critical properties of the solvent and generalized expressions of the acentric factor. When extended to mixtures, the van der Waals one-fluid mixing rules along with the Berthelot combining rule for the molecular cross energy parameter are used. The arithmetic mean combining rule is used for the cross co-volume parameter. A correction to the Berthelot combining rule which is obtained from vapor-liquid equilibrium data of polymer solutions is used for predicting the upper critical solution temperatures for many different binary polymer solutions, including polar and non-polar systems. The results are remarkably successful. Typically, the difference between the predicted and the experimental upper critical solution temperatures is less than twenty degrees. Further, in all cases, correlation is achieved in an easy and straightforward way without difficulty and excellent results are obtained. Unlike other theories and models, the van der Waals equation of state is capable of predicting the flatness of the coexistence curves, which often occurs in polymer solutions.