The problem describes an inverse proportionality between the time taken for a kettle to boil and the power of the kettle.

Given:

• Time $t$ is inversely proportional to power $P$, so $t \propto \frac{1}{P}$, or $t = \frac{k}{P}$, where $k$ is a constant.
• For a 2000 W kettle, it takes 180 seconds to boil water: $t = 180$ s, $P = 2000$ W.

We can find the constant $k$ using the formula:

$t = \frac{k}{P} \implies k = t \times P$

Now, calculate $k$ using the known values:

$k = 180 \times 2000 = 360000$

Next, to find the time $t_2$ for the 1600 W kettle, we use the same formula:

$t_2 = \frac{k}{P_2}$

Substitute $k = 360000$ and $P_2 = 1600$ W:

$t_2 = \frac{360000}{1600} = 225 \text{ seconds}$

Thus, it would take 225 seconds for the 1600 W kettle to boil a litre of water.

Would you like further details or explanations?

Here are 5 related questions to deepen your understanding:

1. How does increasing the power of the kettle affect the boiling time?
2. What would happen to the time if the power was reduced by half?
3. Can you derive a general formula to calculate the boiling time for any kettle power?
4. How would you approach the problem if the water quantity were different?
5. What are the practical limitations of this inverse proportionality in real-life scenarios?

Tip: In inverse proportionality, if one quantity increases, the other decreases, and vice versa.