Question 1188017
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FOUR MEN AND 8 WOMEN CAN FINISH A PIECE OF WORK JOINTLY IN 5 DAYS WHILE 3 MEN AND 2
WOMEN CAN FINISH THE SAME WORK JOINTLY IN 10 DAYS. FIND THE TIME TAKEN BY ONE MAN
ALONE AND THAT OF ONE WOMAN ALONE TO FINISH THE SAME WORK.
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<pre>
Let m be the rate of work of one man and let w be the rate of work of one woman.


Then we have this system of 2 equations in 2 unknowns


    4m + 8w = {{{1/5}}}     (1)

    3m + 2w = {{{1/10}}}    (2)


To run of the denominator, I will multiply eq(1) by 5 (both sides) and will multiply eq(2) by 20.
I will get then


    20m + 40w = 1           (3)

    60m + 40w = 2           (4)


Next, I will subtract eq(3) from eq(2).  I will get


    40m = 1,   hence  m = {{{1/40}}}.


Now from eq((3),

    {{{20*(1/40)}}} + 40w = 1,


which gives then

    40w = 1 - {{{20/40}}} = {{{1/2}}},   w = {{{1/80}}}.


The problem is just solved: a single man will do the job in 40 days, working alone;

                            a single woman will do it in 80 days.
</pre>

Solved.