1. **State the problem:** The time taken for a kettle to boil is inversely proportional to its power. Given that a 2000 W kettle takes 180 seconds to boil, find the time for a 1600 W kettle. 2. **Set up the inverse proportionality:** Let $t$ be the time in seconds and $P$ be the power in Watts. Since $t$ is inversely proportional to $P$, we write: $$ t \propto \frac{1}{P} $$ This means: $$ t = \frac{k}{P} $$ where $k$ is a constant. 3. **Find the constant $k$ using the given data:** For $P=2000$ W and $t=180$ s, $$ 180 = \frac{k}{2000} \implies k = 180 \times 2000 = 360000 $$ 4. **Calculate the time for $P=1600$ W:** $$ t = \frac{360000}{1600} = 225 \text{ seconds} $$ 5. **Interpretation:** It will take 225 seconds for the 1600 W kettle to boil a litre of water. **Final answer:** $$\boxed{225 \text{ seconds}}$$