Question

the number of hours required to build a fence is inversely proportional to the number of people working on the fence.
if it takes 7 people, 68 hours to complete the fence, then how long will it take 18 people to build the fence?
round your answer to 2 decimal places if needed.

hours
question help: □ video

Explanation:

Step1: Define inverse proportion formula

Let $h$ = hours, $p$ = number of people. Inverse proportion: $h = \frac{k}{p}$, where $k$ is constant.

Step2: Solve for constant $k$

Substitute $h=68$, $p=7$:
$68 = \frac{k}{7}$
$k = 68 \times 7 = 476$

Step3: Calculate hours for 18 people

Substitute $k=476$, $p=18$:
$h = \frac{476}{18}$

Answer:

26.44 hours