The time it takes to finish a job varies inversely as the number of workers helping with the job. If 8 workers require 12 hours to finish a job, how much time would 18 workers require to finish the same job?
To solve this problem, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases proportionally, and vice versa.
Let's start by defining the variables involved:
Let t represent the time it takes to finish the job.
Let w represent the number of workers helping with the job.
According to the problem, the time and the number of workers vary inversely, which can be represented by the equation:
t = k/w
where k is a constant of variation.
To find the value of k, we can use the given information. When there are 8 workers, it takes 12 hours to finish the job. Plugging this into the equation, we get:
12 = k/8
To solve for k, we multiply both sides of the equation by 8:
96 = k
Now that we have the value of k, we can find the time it would take with 18 workers:
t = 96/18
Simplifying this expression:
t = 5.33 hours
Therefore, 18 workers would require approximately 5.33 hours to finish the same job.
wt = k
So, you want t such that
18t = 8*12