Question 76623
The rate that the job is getting done by thge 10 men and 15 women
is 1 job / 6 days. I'll say that the rate that 1 man is doing the job
is {{{1/m}}} jobs/day and the rate that 1 woman is doing the job is
{{{1/w}}} jobs/day.
10 men are working 10 times as fast and 15 women are working 15 times
as fast.
So, the rate 10 men are working is {{{10*(1/m)}}}. The rate that
15 women are working is {{{15*(1/w)}}} therefore
{{{1/6 = 10*(1/m) + 15*(1/w)}}}
The problem tells me that 1 man does the job in 100 days, so
{{{1/m = 1/100}}}
{{{1/6 = 10*(1/100) + 15*(1/w)}}}
{{{1/6 = 1/10 + 15/w}}}
multiply both sides by the LCD, 30w
{{{5w = 3w + 30*15}}}
{{{2w = 450}}}
{{{w = 225}}}
So, {{{1/w = 1/225}}}. It takes 1 woman 225 days to do the job alone.
check
{{{1/6 = 10*(1/100) + 15*(1/225)}}}
{{{1/6 = 1/10 + 1/15}}}
{{{5/30 = 3/30 + 2/30}}}
OK