During the labor day weekend, amy and kathleen each ran in a race. amy ran in a 5k and completed it in 31 minutes and 15 seconds. kathleen ran in a half-marathon, which is 21.1 kilometers, and completed it in 2 hours, 11 minutes, and 52.5 seconds.

let d represent distance in kilometers, r represent the rate, and t represent time in minutes. the proportional relationship can be used to determine the speed at which amy and kathleen ran their respective races. using amy's distance and time, the proportional relationship can be used to determine her rate. using kathleen's distance and time, the proportional relationship can be used to determine her rate. based on the actual rates that they ran during their respective races, amy ran at kathleen.