Question

When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 19 days by 35 workers. How many days would it take to build a similar house with 5 workers?

Answer 1

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation $y=\frac{k}{x}$ represents the relation where y is inversely proportional to x and k is the constant of proportionality.  

So our required equation would be $d=\frac{k}{n}$

Upon substituting our given values, we will get:

$19=\frac{k}{35}$

$k=19\cdot 35$

$k=665$

Since constant of proportionality is 665, so our equation would be $d=\frac{665}{n}$.

To find the number of days it will take to build a similar house with 5 workers, we will substitute $n=5$ in our equation as:

$d=\frac{665}{5}$

$d=133$

Therefore, it will take 133 days for 5 workers to build a similar house.