Question 909162
Start with the rate for 20 women in 14 days.  The one-woman rate is {{{1/(20*14)}}} jobs per day.


Each child has a rate half of one woman, so the child rate is {{{1/(2*20*14)}}}.


Simplify those rates.
Woman, {{{1/280}}}
Child, {{{1/560}}}


Compare with the men.
Let r = the one-man rate.
{{{3(r)=5(1/280)}}}, which is R*T for each of these two groups, the three men compared to the five women;
{{{r=5(1/280)(1/3)}}}
{{{r=5/840}}}
{{{r=1/168}}}


Summary of each one-person work rate:
Man, {{{highlight(1/168)}}}
Woman, {{{highlight(1/280)}}}
Child, {{{highlight(1/560)}}}


QUESTION:  In how much time in days, {{{t}}} for 6 men, 5 women, and 5 children?  ONE job.

{{{(6(1/168)+5(1/280)+5(1/560))t=1}}}
{{{(6/168+5/280+5/560)t=1}}}
Start simplifying
{{{(1/28+1/56+1/112)t=1}}}
LCD is 112
{{{(4/112+2/112+1/112)t=1}}}
{{{(7/112)t=1}}}
{{{(1/16)t=1}}}
{{{highlight(t=16)}}}, DAYS