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
18 * 6 = 12 * ?
how many worker days needed?
18 * 6 worker days/job
so
12 workers * x days = 18 *6
x = 18/2
To solve this problem, we need to find the value of the constant k. We can do this by using the given information that 18 workers can finish the job in 6 days.
Using the equation T = k/w, we can substitute the values T = 6 (days) and w = 18 (workers). Let's solve for k:
6 = k/18
To find the value of k, we can cross multiply:
6 * 18 = k
k = 108
Now that we have the value of k, we can use it to solve the second part of the problem.
We need to find how many days it will take 12 workers to do the same job. We can use the same equation T = k/w, but this time we will use w = 12 (workers). Let's solve for T:
T = 108/12
T = 9
Therefore, it will take 12 workers 9 days to do the same job.
The correct answer is option B) 9 days.