SOLUTION: 16 workers are able to paint 12 cupboards in 6 days. How many days would it take for 12 workers to paint 45 cupboards?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 16 workers are able to paint 12 cupboards in 6 days. How many days would it take for 12 workers to paint 45 cupboards?       Log On


   

Question 985130: 16 workers are able to paint 12 cupboards in 6 days. How many days would it take for 12 workers to paint 45 cupboards?
Found 2 solutions by ikleyn, macston:
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!

From the given data, the rate of work for  1  worker per  1  day is   12%2F%2816%2A6%29 = 12%2F96 = 1%2F8 cupboards%2F%28worker%2Aday%29.
In other words,  1  worker paints  1%2F8  of a cupboard per day.

(We assume that all workers have the same rate of work and that all cupboards are identical).

If 12 workers paint  45  cupboards in  x  days, then their rate of work is  45%2F%2812%2Ax%29 cupboards%2F%28worker%2Aday%29.

It the same rate of work as calculated above, i.e. 1%2F8 cupboards%2F%28worker%2Aday%29.
Thus you have an equation

45%2F%2812%2Ax%29 = 1%2F8.

Hence,  x = %2845%2A8%29%2F12 = 30 days.

Answer.  30 days.


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
((16 workers)(6 days))/12 cupboards=8 worker-days/cupboard
It takes 8 worker-days to paint 1 cupboard.
.
((45 cupboards)(8 worker-days/cupboard))/12 workers=30 days
ANSWER: It will take 12 workers 30 days to paint 45 cupboards.