check my work please
For his business, Gil has determined that the time it takes to finish a job varies inversely with the number of workers. This can be expressed as:
==\ensuremath{T=\frac{k}{w}}== where T = time, k is a constant, and w = number of workers. Gil’s records show that 18 workers can finish a job in 6 days. How many days will it take 12 workers to do the same job?
A 4
B 9***
C 12
D 36
yes
18*6 = 9*12
But two of us already went through that.
To solve this problem, we can use the given formula for the relationship between time and number of workers:
T = k/w
Where T represents the time it takes to finish a job, k is a constant, and w represents the number of workers.
Given that Gil's records show that 18 workers can finish a job in 6 days, we can use this information to determine the value of the constant k.
Using the given values:
T = 6 days
w = 18 workers
Plugging these values into the formula, we get:
6 = k/18
To find the value of k, we can cross-multiply and then solve for k:
6 * 18 = k
k = 108
Now that we have determined the constant k, we can use it to find the number of days it will take for 12 workers to complete the same job.
Using the formula:
T = k/w
Plugging in the values:
k = 108
w = 12 workers
T = 108/12 = 9
Therefore, it will take 12 workers 9 days to complete the same job. So the correct answer is option B: 9.