# Thread: Linear Equation with two variables

1. ## Linear Equation with two variables

Need help to solve this problem:

2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish the work in 3 days. Find the time taken by 1 woman alone and also that taken by 1 man alone.

2. I'm a little rusty on this, so this might be wrong.

We know that working rate times time equals the amount of work done, and in the case we can say that finishing an embroidery counts as 1 work done. Also, 3 men working 1 day is that same as 1 man working 3 days.

Let W be the workrate for a woman and M the workrate for a man. Then
the first equation can be written as:

$2(4)(W) + 5(4)(M) = 1$
2 for the number of people, and 4 for the hours worked, so the second equation is
$3(3)(W) + 6(3)(M) =1$
Since they both equal 1, they are equal to each other,
$8W+20M = 9W +18M$
Simplifying,
$1W=2M$
So woman work twice as fast as men. We can plug this into the original equation.
$8W+20M = 8W+10W=1$
$W=1/18$
Then we can solve for M
$W=2M=1/18$
$M=1/36$

So it takes a woman 18 days to finish the job, and a man 36 days to finish the job.

3. ## Thanks

Thank you for the solution.