Three experiments used delay conditioning of magazine approach in rats to examine the summation of responding when two conditioned stimuli (CSs) are presented together as a compound. The duration of each CS varied randomly from trial-to-trial around a mean that differed between the CSs. This meant that the rats' response rate to each CS was systematically related to the reinforcement rate of that CS, but remained steady as time elapsed during the CS (Harris & Carpenter, 2011; Harris, Gharaei, & Pincham, 2011). When the rats were presented with a compound of two CSs that had been conditioned separately, they responded more during the compound than during either of the CSs individually. More significantly, however, in all three experiments, the rats responded to the compound at the same rate as they responded to a third CS that had been reinforced at a rate equal to the sum of the reinforcement rates of the two CSs in compound. We discuss the implications of this finding for associative models (e.g., Rescorla & Wagner, 1972) and rate-based models (Gallistel & Gibbon, 2000) of conditioning.