Question

When building a house, the number of days required to build is inversely proportional to with the number of workers. One house was built in 72 days by 5 workers. How many days would it take to build a similar house with 18 workers.

Answer 1

Let the number of day is expressed as d and number of workers as w.

So relation between number of workers and number of days is,

$\begin{gathered} n\propto\frac{1}{w} \\ n=k\frac{1}{w} \\ n=\frac{k}{w} \end{gathered}$

Substitute 72 for d and 5 for w in the equation to obtain the value of k.

$\begin{gathered} 72=\frac{k}{5} \\ k=72\cdot5 \\ =360 \end{gathered}$

The equation is,

$n=\frac{360}{w}$

Substitute 18 for w to determne the number of day.

$\begin{gathered} n=\frac{360}{18} \\ =20 \end{gathered}$

So 20 days are required to build a house with 18 workers.

Answer is 20 days.