Question

Formulate the following problem as a pair of equations and hence find their solutions. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work and also that taken by 1 man alone.

Answer 1

Let $w$ and $m$ represent women and men respectively.

$2w+5m$ can do $1$ work in $4$ days

$2w+5m$ can do $\frac{1}{4}$ work in $1$ days

Also $3w+6m$ can do $1$ work in $3$ days

$3w+6m$ can do $\frac{1}{3}$ work in $1$ days

Then equating work with men and women,

$\Rightarrow 2w+5m=\frac{1}{4}...........\left(1\right)$

$3w+6m=\frac{1}{3}$

$\Rightarrow w+2m=\frac{1}{9}.........\left(2\right)$

By doing $\left(1\right)-2\times \left(2\right)$

$\Rightarrow m=\frac{1}{4}-\frac{2}{9}=\frac{9-8}{36}=\frac{1}{36}$

$w=\frac{1}{9}-\frac{1}{18}=\frac{1}{18}$

$\Rightarrow 1$ man can do $\frac{1}{36}$ work in $1$ days

$1$ man can do $1$ work in $36$ days

$1$ woman can do $\frac{1}{18}$ work in $1$ days

$1$ woman can do $1$ work in $18$ days

$\therefore 1$ man can do in $36$ days and

$1$ woman can do $18$ days.

Hence, solve.