Cooking times don't always scale proportionally because they depend more on the thickness and internal temperature of the food than the overall quantity. A smaller roast chicken won't cook in one-quarter the time of a larger one because it still needs to reach a safe internal temperature.
When scaling down a recipe, it's tempting to assume that cooking times will decrease proportionally. However, this isn't always the case, especially for dishes where the cooking time is dictated by the food's internal temperature or structural changes.
Consider a roast chicken. The primary goal is to cook the chicken to a safe internal temperature (e.g., 165°F or 74°C in the thickest part of the thigh). A larger chicken has a greater mass and therefore takes longer for heat to penetrate to its center. However, a smaller chicken, while having less mass, still requires the same internal temperature to be reached for safety and proper cooking. The heat still needs to penetrate through a certain thickness of meat.
Similarly, baking a cake involves structural changes. The heat needs to set the proteins and starches, and this process takes time regardless of whether you're baking a large cake or a small cupcake. While a cupcake will bake faster than a cake, it won't be proportionally faster based solely on the difference in volume.
Recipes involving liquids, like soups or sauces, might see a more proportional reduction in cooking time, especially if the primary goal is to reduce the liquid volume. However, even here, factors like the surface area of the pot and the desired consistency can influence the cooking time.
Always use a food thermometer to check the internal temperature of meats and baked goods, especially when scaling recipes. Don't rely solely on the original cooking time; start checking for doneness earlier than you think you should, and adjust as needed.