Question

$2$ Women and $5$ men can together finish a piece of embroidery in $4$ days, while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ women alone to finish the embroidery, and that taken by $1$ man alone.

Answer 1

Let $a$ represents the women and $b$ represents the men. Then $2a+5b$ can do work in 4 days that means, $\frac{1}{4}$ work can be done in 1 day. Similarly, $3a+6b$ can do $\frac{1}{3}$ work in 1 day. So,

$2a+5b=\frac{1}{4}$ (1)

$3a+6b=\frac{1}{3}$ (2)

$a+2b=\frac{1}{9}$ (3)

Subtract equation (1) from (2),

$a+b=\frac{1}{12}$ (4)

From equation (3) and (4),

$b=\frac{1}{36},a=\frac{1}{18}$

This shows that 1 man alone can do 1 work in 36 days and one woman alone can do 1 work in 18 days.