### Work & workers word problem

Here's another one of those job / workers word problems (inverse or direct variation). Try and see if you can solve it using the "table" method instead of equations:

Again, we can set up a table and reason this out. Initially set it up like this:

Then think of the "days" column. We want to "go" from 26 to 12. You could use a proportion here... or first figure out how many clerks are needed to do this job in 2 days, and then from that go to 12 days.

If 18 clerks do it in 26 days, then how many clerks would do it in 2 days... which is 1/13 the amount of time.... so we need 13 times as many clerks.

13 x 18 = 234 clerks are needed.

Now, if 234 clerks do it in 2 days, how many clerks would do it in 12 days? Now, the time increases 6-fold, so we need only 1/6 as many workers.

234 / 6 = 39.

So 39 clerks are needed.

*A certain job can be done by 18 clerks in 26 days. How many clerks are needed to perform the job in 12 days?*Again, we can set up a table and reason this out. Initially set it up like this:

jobs | clerks | days -------------------------- 1 | 18 | 26 -------------------------- 1 | | -------------------------- 1 | ? | 12

Then think of the "days" column. We want to "go" from 26 to 12. You could use a proportion here... or first figure out how many clerks are needed to do this job in 2 days, and then from that go to 12 days.

If 18 clerks do it in 26 days, then how many clerks would do it in 2 days... which is 1/13 the amount of time.... so we need 13 times as many clerks.

13 x 18 = 234 clerks are needed.

jobs | clerks | days -------------------------- 1 | 18 | 26 -------------------------- 1 | 234 | 2 -------------------------- 1 | ? | 12

Now, if 234 clerks do it in 2 days, how many clerks would do it in 12 days? Now, the time increases 6-fold, so we need only 1/6 as many workers.

234 / 6 = 39.

So 39 clerks are needed.