Your senses are better than any timer. Poke one with a fork: it should slide in with slight resistance. Bite one: it should have a clean snap but no raw crunch. If it bends like a wet noodle, you’ve gone too far. Use the “color test”: raw carrots are pale orange; cooked ones turn a deeper, more vibrant hue.
Fun fact: the phrase “carrot and stick” comes from the idea of dangling a carrot to motivate a donkey—but I prefer to think of the carrot as the reward itself. Getting the texture right is your prize.