AndreG wrote:

Hm, i got stuck cuz I got something a little different:

YOURS: 3 men would do the same work 5 days sooner than 9 women --> \frac{m}{3}+5=\frac{w}{9}.

MINE: 3 men would do the same work 5 days sooner than 9 women --> \frac{3}{m}=\frac{9}{w}+5

In the above equation you also have for 2 men: \frac{2}{m} - so why do u suddenly use the reciprocal? And why don't we add the 5 to women, because they take longer, hence their side is smaller...

Let one woman complete the job in

w days and one man in

m days.

First equation:It takes 6 days for 3 women and 2 men working together to complete a work:

As the rate of 1 woman is

\frac{1}{w} job/day, then the rate of 3 women will be

\frac{3}{w} job/day. As the rate of 1 man is

\frac{1}{m} job/day, then the rate of 2 men will be

\frac{2}{m} job/day. Combined rate of 3 women and 2 men in one day will be:

\frac{3}{w}+\frac{2}{m} job/day.

As they do all the job in 6 days then in 1 day they do 1/6 of the job, which is combined rate of 3 women and 2 men -->

\frac{3}{w}+\frac{2}{m}=\frac{1}{6}.

Second equation:3 men would do the same work 5 days sooner than 9 women:

As 1 man needs

m days to do the job 3 men will need

\frac{m}{3} days to do the job. As 1 woman needs

w days to do the job 9 women will need

\frac{w}{9} days to do the job. 3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job, hence

\frac{m}{3} is 5 less than

\frac{w}{9} -->

\frac{m}{3}+5=\frac{w}{9}.

Hope it's clear.

My question is this, on the second equation how did you KNOW to put m/3, whereas in the first it was 2/m?

In the first equation, you know that a man does 1/m of the job, and that 2 would do 2/m. In the second equation the rate is still 1/m, but you have 3 men, so should it not be 3/m+5=9/m?