Question

the time that a group of carpenters takes to build a deck is inversely proportional to the number of carpenters. if 3 carpenters can build a deck in 36 working hours, how many carpenters are needed to build a deck in 27 working hours? 3 4 6 5 2

Explanation:

Step1: Define inverse proportionality

Let $t$ = time in hours, $n$ = number of carpenters. Inverse proportionality means $t = \frac{k}{n}$, where $k$ is the constant of proportionality.

Step2: Solve for constant $k$

Substitute $t=36$, $n=3$ into the formula:
$36 = \frac{k}{3}$
$k = 36 \times 3 = 108$

Step3: Find required number of carpenters

Substitute $t=27$, $k=108$ into $t = \frac{k}{n}$:
$27 = \frac{108}{n}$
$n = \frac{108}{27} = 4$

Answer:

B. 4