The long-range correlations between the transverse momenta (pT) and the multiplicities (n) of charged particles in two windows separated in rapidity are analyzed in the framework of the model with independent emitters (strings) of two types. Primary emitters are produced immediately in collision and secondary - after the interaction of some of the first ones. The mechanism of the emergence of secondary emitters is simulated by a simple toy model. The dependencies of the n-n and pT-n correlations on the average number of primary emitters and on the parameter characterizing the strength of the interaction between them were studied. It was shown that with the increase of interaction parameter both the increase and the decrease of the n-n correlation strength are possible depending on the model parameters. The possibility of the model description of the experimentally observed negative pT-n correlations is discussed. The obtained analytical results were also tested by the Monte-Carlo simulations.