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?

Question

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

Answer 1

T=KW so solve for k to use in question 6=x(18) x=1/3

So T=(1/3)(12) T=4

Answer 2

To solve this problem, we need to use the given formula for the relationship between time and the number of workers:

T = k/w

We are given that when there are 18 workers, the job takes 6 days to complete. Let's plug these values into the formula:

6 = k/18

To find the value of k, we can cross-multiply:

6 * 18 = k

k = 108

Now we can use this value of k to find the time it will take for 12 workers to complete the job. Plug in the new values:

T = 108/12

T = 9

So it will take 12 workers 9 days to complete the job. Therefore, the answer is option B: 9.