8 men can build a house in 6 months how long will it take 12 men tovdo the same job working at the same rate?
the time taken would be inversely proportional to the number of men, that is , the men we have working the less time it takes.
t = k/m
k = tm
given: 8 men take 6 months
k = 6x8 = 48
when m = 12
t = 48/12 = 4
or
number of "man-months" = 48
time for 12 men = 48/12 = 4 months
To find out how long it will take 12 men to build the house, we can use the concept of man-months.
Given that 8 men can build a house in 6 months, we can calculate the number of man-months required to build the house using the formula:
Man-months = Number of men × Number of months
For the first case, with 8 men working for 6 months:
Man-months = 8 × 6 = 48
Now, to find out how long it will take 12 men to do the same job, we can rearrange the formula:
Number of months = Man-months / Number of men
For the second case, with 12 men:
Number of months = 48 / 12 = 4
Therefore, it will take 12 men to build the house in 4 months, assuming both groups work at the same rate.
To solve this problem, we can use the concept of man-hours. The number of man-hours required to complete the job is constant, regardless of the number of men working.
Given that 8 men can complete the job in 6 months, we can calculate the total man-hours required for the job by multiplying the number of men by the number of months:
Total man-hours = Number of men * Number of months
Total man-hours = 8 men * 6 months
Total man-hours = 48 man-months
So we know that the job requires 48 man-months to complete.
Now, let's consider the situation with 12 men. Since the number of men has increased, we need to figure out how many months it will take for the 12 men to complete the job while working at the same rate.
To find the answer, we'll divide the total man-hours required by the number of men:
Months required = Total man-hours / Number of men
Months required = 48 man-months / 12 men
Months required = 4 months
Therefore, it would take 12 men working at the same rate as the initial 8 men approximately 4 months to complete the job.