Question

The time it takes to finish a job varies inversely with the number of workers. Six (6) workers require 10 hours to finish a job. What equation represents how long it would take n workers to finish a job?(1 point)
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Answer 1

To represent the time it takes to finish a job in relation to the number of workers, we can use the concept of inverse variation. If the time \( T \) taken to complete a job varies inversely with the number of workers \( n \), we can express this relationship as:

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

This can be converted into an equation by introducing a constant \( k \):

\[
T \cdot n = k
\]

To find \( k \), we can use the information given: with 6 workers, the time taken is 10 hours. Plugging these values into the equation gives us:

\[
10 \cdot 6 = k \implies k = 60
\]

Now, substituting \( k \) back into the equation, we have:

\[
T \cdot n = 60
\]

To find the equation that represents how long it would take \( n \) workers to finish the job, we can solve for \( T \):

\[
T = \frac{60}{n}
\]

Thus, the equation that represents how long it would take \( n \) workers to finish the job is:

\[
T = \frac{60}{n}
\]