We propose a reduced model of proteins and simulate folding of a designed three helix bundle protein with 54 residues, the dynamics of a random heteropolymer, and the helix formation of a short peptide, up to similar to 1 mu s, near the estimated lower bound of folding time. The model has explicit backbone atoms, while solvent effects are taken into account via effective potentials. Interactions include two multibody terms; (1) the hydrogen bond strength reflecting the local dielectric constant that is dependent on protein configuration and (2) the hydrophobic force which depends on the local density of peptide atoms imitating the solvent accessible surface area model of hydrophobic force. With this model, all trajectories of a designed protein reach a native like conformation within 0.5 mu s although they exhibit some remaining residual fluctuations. On the other hand, a random polymer collapses to several nonspecific compact forms and continues to change its global shape. A 16 residue segment forming a helix in the designed protein does not stably form a helix when it is cleaved, illustrating the effect of nonadditivity.