The time taken to paint a school varies inversely with the number of painters completing the task - HSC - SSCE Mathematics Standard - Question 9 - 2024 - Paper 1

The time taken to paint is inversely proportional to the number of painters. We can express this as:

$T = \frac{k}{P}$

where:

• $T$ is the time in days,
• $P$ is the number of painters,
• $k$ is a constant.

When 6 painters take 20 days, we find:

$k = T \times P = 20 \times 6 = 120 \text{ painter-days}$