We present the results of a nonrelativistic constituent quark model study of the semileptonic decays Lambda(b)(0)-->Lambda(c)(+)l(-)(ν) over bar (l) and Xi(b)(0)-->Xi(c)(+)l(-)(ν) over bar (l) (l=e,mu). We work on coordinate space, with baryon wave functions recently obtained from a variational approach based on heavy quark symmetry. We develop a novel expansion of the electroweak current operator, which supplemented with heavy quark effective theory constraints, allows us to predict the baryon form factors and the decay distributions for all q(2) (or equivalently w) values accessible in the physical decays. Our results for the partially integrated longitudinal and transverse decay widths, in the vicinity of the w=1 point, are in excellent agreement with lattice calculations. Comparison of our integrated Lambda(b)-decay width to experiment allows us to extract the V-cb Cabbibo-Kobayashi-Maskawa matrix element for which we obtain a value of \V-cb\=0.040+/-0.005(stat)(-0.002)(+0.001)(theory) also in excellent agreement with a recent determination by the DELPHI Collaboration from the exclusive (B) over bar (0)(d)-->D(*+)l(-)(ν) over bar (l) decay. Besides for the Lambda(b)(Xi(b))-decay, the longitudinal and transverse asymmetries and the longitudinal to transverse decay ratio are <a(L)>=-0.954+/-0.001(-0.945+/-0.002), <a(T)>=-0.665+/-0.002(-0.628+/-0.004), and R-L/T=1.63+/-0.02(1.53+/-0.04), respectively.