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.
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