It takes 12 men 5 days to complete a job. Work out how many days it would take 3 men to complete a job?

Question

Help. This is really hard

Answer 1

In this situation, the number of men and the time it takes varies jointly with the number of completed jobs.  If m = # of men, t = time (# of days), and J = # of jobs, the function would be:

 

J = k·m·t

 

(Note: k is a constant that helps us relate the variables.  In this case it is equivalent to how much of the job one worker could complete in one day.)

 

In this problem, the first sentence allows us to fill in the equation and find k.  (This is always the first step.)

 

1 = k·12·5

1 = 60k

1/60 = k

 

To answer the question, use the information provided in the second step, as well as the value of k.

 

1 = (1/60)·3·t

1 = 3t/60

60 = 3t

t = 20

 

It will take 3 men 20 days to complete the job.