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.

[tex]t=\frac{k}{w}[/tex]
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:
[tex]24=\frac{k}{5}[/tex]
which gives k = 120.
If the required time to complete the project is 15 days, the equation becomes:
[tex]15=\frac{120}{w}[/tex]
Solving for w, gives w = 120/15 = 8 workers.

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anuksha0456 anuksha0456 · Answer 2 · 2022-06-02T14:34:40+02:00

The required inverse variation equations are:

t = 120/k or k = 120/t,

where t is the time for the project and k is the number of workers.

To complete the work in 15 days, the company will need 8 workers.

What are direct and inverse proportions?

Two terms are directly proportional when the increase in one increases the other term, and the decrease in one decreases the other term.

Two terms are inversely proportional when the increase in one decreases the other term and the decrease in one increases the other term.

How do we solve the given question?

In the question, we are given that the time to complete a project is inversely proportional to the number of people who are doing the project.

5 people complete the project in 24 days, so one person will complete the project in 5*24 = 120 days.

We are asked to give an inverse variation equation.

Let the number of people be k, and the time taken to complete the project be t.

We know that k and t are inversely related, that is, t ∝ 1/k or k ∝ 1/t.

To remove the sign of proportionality, we multiply the R.H.S. by 120 (the days taken by a single person), which will give us the required inverse variation equation as:

t = 120/k or k = 120/t.

Now, using the above equation, we can easily find the number of workers the company will need to complete the project in 15 days.

Given: t = 15, k = ?

k = 120/t = 120/15 = 8.

∴ The company will need 8 workers to complete the project in 15 days.

Learn more about direct and inverse proportions at

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