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:
\[ T = \frac{60}{n} \]
1 answer