ajay.05 said:
Homework Statement
2 women and 5 men can finish a work a work 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 work, and also that taken by 1 man alone.
Homework Equations
Pair of linear equations in two variables
The Attempt at a Solution
I can't figure how can I do it out:( LOL
But in the solution, I saw that it had been given that,
Work done by woman in 1 day=x
Work done by man in 1 day=y
=>2/x+ 5/y =1/4
=>3/x + 6/y =4/3
Solving them, gave the answers. But, my doubt here is, how did 2/x,5/y,etc. arrive?
Could anybody please enlighten me:)
I think the confusion comes from the units in your problem set up.
Your setup says
x is the work done by a woman in 1 day, so I take units are [work woman##^{-1}## day##^{-1}##].
If so, then the work per day by 2 women would be: 2 [women] *
x [work woman##^{-1}## day##^{-1}##] = 2
x [work day##^{-1}##].
Then the first equation would be 2
x + 5
y = 1/4 [work / day]. This is the way I'd do the problem.
However, if you follow the problem statement in choosing your variables:
Let
x = the time taken by 1 woman alone to finish the work. Then
x has units [woman days work##^{-1}##].
Similarly, let
y be the time for a 1 man alone [man days] to finish the work.
It follows that 2 [women] /
x [woman days work##^{-1}##] has units [work days##^{-1}##], and you get the equations that you posted (with a 1/3 on the RHS as the previous poster points out).
As some of the other posters noticed, these aren't linear equations. That's why it seems easier to me to do it the other way, with your original definition:
x is work/woman/day, and so on.
