We present new quasi-elastic neutron scattering experiments and simulation analysis for studying the hydration water dynamics of N-acetyl-leucine-methylamide (NALMA) solutions as a function of concentration and temperature. The experiments show non-Arrhenius translational dynamics over the temperature range of -3 to +37 degreesC for all concentrations, and fits to the experimental intermediate scattering function show nonexponential relaxation dynamics. While the lower-concentration NALMA solution could be classified as an intermediate to strong liquid, the higher concentration is legitimately defined as a fragile liquid, and the hydration dynamics of the most concentrated solution exhibits very good correspondence with the same signatures of non-Arrhenius behavior and nonexponential dynamics as that observed for supercooled water well below -20 degreesC. The corresponding molecular dynamics simulation analysis of the high concentration data using the SPC water model, a common companion water model used in protein simulations, is severely limited in application to the dynamics of this system because of the very low temperature of maximum density of the SPC water model. However, the simulations are informative in the sense that nonexponential relaxation is still evident at the effectively higher temperatures, which indicates that the underlying potential energy surface is very rough at high concentrations, although the sampling is still sufficiently ergodic so that Arrhenius behavior is observed. We provide discussion in regards to the mutually beneficial connection between supercooled liquids and glasses and its biological importance for protein-water systems.