The time to complete a project varies inversely with the number of employees. If 6 people can complete the project in 4 days, how long will it take 8 people?

2 days

6 days

3 days

5 days

1 answer

The time to complete a project varies inversely with the number of employees, which can be expressed mathematically as:

\[ T \propto \frac{1}{N} \]

where \( T \) is the time to complete the project and \( N \) is the number of employees.

From the information given:

  • 6 people can complete the project in 4 days.

We can establish a relationship using the formula:

\[ T \times N = k \]

where \( k \) is a constant.

So, with 6 people working for 4 days:

\[ 4 \times 6 = k \] \[ k = 24 \]

Now we want to find the time \( T \) when there are 8 people:

\[ T \times 8 = 24 \]

To solve for \( T \), divide both sides by 8:

\[ T = \frac{24}{8} = 3 \text{ days} \]

Thus, it will take 8 people 3 days to complete the project.

The answer is 3 days.