Question

the time t, in hours, required to paint a house is inversely proportional to the number of painters, p. if it takes 20 hours for 3 painters to paint a house, how long will it take 5 painters to paint the same house?

Explanation:

Step1: Define inverse proportion

For inverse proportionality, $t = \frac{k}{p}$, where $k$ is the constant of proportionality.

Step2: Solve for constant $k$

Substitute $t=20$, $p=3$:
$20 = \frac{k}{3}$
$k = 20 \times 3 = 60$

Step3: Calculate time for 5 painters

Substitute $k=60$, $p=5$ into $t = \frac{k}{p}$:
$t = \frac{60}{5} = 12$

Answer:

12 hours