Question

A factory employs 18 women to sew 540 dresses. The women take 6 weeks to do the job. If 12

women had been employed instead, how many weeks would it have taken them to sew the 540
dresses?

Answer 1

9514 1404 393

Answer:

9 weeks

Explanation:

In problems of this nature, the usual assumption is that the time required is proportional to the work product and inversely proportional to the number of people doing the job. Here, there is no change in the amount of work, but the number of people is reduced by a factor of 12/18 = 2/3.

So, the amount of time required is expected to increase by a factor of 1/(2/3) = 3/2.

(6 weeks)×(3/2) = 9 weeks

It would have taken 9 weeks to sew the 540 dresses.