The time, T seconds, it takes a water heater to boil a constant mass of water is inversely proportional to the power, P watts, of the water heater. When P is 300, T is 20. What is T when P is 400?

This is a question regarding inverse proportion. This is when one value increases as the other decreases.

For this question, the equation can be written as:

T ∝ 1/P

The directly proportional sign (∝) can be replaced with an equals and a constant, k to give:

T = k/P

Using the specific numbers provided in the question we can work out the constant, k:

20 = k/300

This can be rearranged to give k as the subject:

k = 20 x 300

k = 6000

Now we can work out the time it takes to boil the water to P = 400 Watts

T = 6000 / 400

T = 15 seconds.