Question

The time to complete a project is inversely proportional to number of people who are doing the project. A certain project can be completed by 5 workers in 24 days. In order to finish the project sooner, the company plans to hire additional workers. How many workers are needed to finish the project in 15 days?
Write an inverse variation equation and solve the problem.

Answer 1

$t=\frac{k}{w}$
where t is the required time to complete the project, k is a constant of proportionality, and w is the number of workers.
Plugging the given values into the equation, we get:
$24=\frac{k}{5}$
which gives k = 120.
If the required time to complete the project is 15 days, the equation becomes:
$15=\frac{120}{w}$
Solving for w, gives w = 120/15 = 8 workers.