The amount of time it takes for a cat to digest the food it eats depends on a number of factors. These factors include type of food eaten (wet vs. dry), fiber level in the food, amount of food eaten, age of the animal, and the activity level of the cat. All of these factors could have an effect on increasing or decreasing the amount of time it takes for the food to move through the digestive tract of the cat. Although there isn't much published research on this topic, from studies in which a dye is added to the food, it can take as long as 9-10 hours before the red dye is seen in the feces. Lastly, the ability to digest food can be compromised as the cat ages. Research has shown that some older cats have limited ability to digest the fat in their diets. Therefore, it's difficult to answer your question with any precision as many factors can affect the amount of time it takes for food to be digested by your cat.