Workload-2

Let the rate of completing a piece of embroidery $W$ by one woman be $x$ . That is if it takes $n$ days for a woman to complete $W$ , then we have $nx = W$ . Similarly, let the rate of completing $W$ by one man be $y$ . Then we have:

$\begin{cases} 4(2x+5y) = 8x + 20y = W &...(1) \\ 3(3x+6y) = 9x+18y = W &...(2) \end{cases}$

$\begin{aligned} (2) \times \frac {10}9: \quad 10x + 20y & = \frac {10}9 W & ...(2a) \\ (2a)-(1): \quad 2x & = \frac 19 W \\ \implies \boxed{18}x & = W \end{aligned}$

Therefore, the number of days one women takes to complete the embroidery is $\boxed{18}$ .

Given 2w+5m in 1 day can complete 1/4th ( eq.1) and 3w+6m in 1 day can complete 1/3rd of the project ( eq.2) From eq1, 1w+2.5m in 1 day can complete 1/8th and from eq2-eq1, 1w+1m can complete 1/12th in one day. From 1w+2.5m=1/8 and 1w+1m=1/12, Multiply 2.5 to 1w+1m=1/12 and we get 2.5w+2.5m=5/24 (eq4) Take eq4-eq1 and we get 1.5w=5/24-1/8=1/12 Hence, 1 woman in 1 day can complete 1/12*2/3 or 1/18th of the project. To complete the entire project by herself, it will take 18 days!