1. The problem states Brett paddled his kayak for 18 minutes at a speed of 80 meters per minute. 2. We want to find the distance Brett moved while the fish swam behind his kayak, which was for one-third of the total time. 3. Calculate the time the fish swam behind the kayak: $$18 \times \frac{1}{3} = 6$$ minutes. 4. Calculate the distance moved in that time using the speed: $$80 \text{ meters/minute} \times 6 \text{ minutes} = 480 \text{ meters}$$. 5. Therefore, the distance Brett moved while the fish was behind him is \textbf{480 meters}.