Question

If $7$ workers can build a trench in $25$ hours, how many workers will be required to do the same work in $35$ hours?

Answer 1

The statement " $y$ varies inversely as $x$ means that when $x$ increases, $y$ decreases by the same factor. In other words, the expression $xy$ is constant:

$xy=k$

where $k$ is the constant of variation.

Let the number of workers be $x$ and the time taken be $y$.

Here, it is given that there are $x=7$ workers who build a trench in $y=25$ hrs. therefore,

$xy=k\Rightarrow 25\times 7=k\Rightarrow k=175$

Thus, the general equation is $xy=175$.

Since $y=35$ hrs, therefore,

$35x=175\Rightarrow x=\frac{175}{35}=5$

Hence, $5$ workers will be required to do the same work in $35$ hours.