The possibility of a contaminant being accidentally or intentionally spilled in a river is a constant concern to those using the water. Methods are developed to estimate: (1) the velocity of a contaminant in a river; (2) the rate of attenuation of the peak concentration of a conservative contaminant; and (3) the time required for a contaminant plume to pass a point. The methods are based on data collected by the U.S. Geological Survey in almost a hundred different rivers representing a wide range of sizes, slopes, and geomorphic types. Although the accuracy of the predictions can be greatly increased by performing time-of-travel studies, the emphasis of this paper is on providing methods for making estimates where few data are available. It is shown that the unit-peak concentration is well correlated with travel time and that the travel time of the leading edge averages 89% of the travel time of the peak concentration.