Final answer:
It will take approximately 12.75 days for 12 machines to complete the job. The calculation is based on the inverse proportionality of machines to days. By calculating the total machine-days of work (153) and dividing it by 12 machines, we find that it will take approximately 12.75 days for 12 machines to complete the job.
Step-by-step explanation:
To find out how long it will take 12 machines to do the job, we can use the concept of machine-hour days. If 9 machines take 17 days to complete the job, then the total number of machine-hour days required is 9 machines x 17 days = 153 machine-hour days. Since the total number of machine-hour days required remains the same, we can set up a proportion:
9 machines x 17 days = 12 machines x t days,
where t is the number of days it will take 12 machines to complete the job. Solving the proportion, we get:
t = (9 machines x 17 days) / 12 machines = 12.75 days.
Therefore, it will take approximately 12.75 days for 12 machines to complete the job.
The calculation is based on the inverse proportionality of machines to days. By calculating the total machine-days of work (153) and dividing it by 12 machines, we find that it will take approximately 12.75 days for 12 machines to complete the job.
If 9 machines take 17 days to complete a job, we can calculate how long it will take for 12 machines to do the same job by understanding the concept of work done and the relationship between machines and time. Specifically, this is an inverse proportion situation where more machines will take less time to complete the same amount of work.
First, find the total work done by multiplying the number of machines by the number of days they work, which gives us a unit of machine-days. In this case, 9 machines taking 17 days amount to 9 * 17 = 153 machine-days of work. This figure represents the total work needed to complete the job.
Second, to find out how long 12 machines will take, we divide the total machine-days of work by the number of machines. Therefore, 153 machine-days divided by 12 machines gives us the answer:
153 / 12 = 12.75 days. Hence, it will take 12 machines approximately 12.75 days to complete the job.