SOLUTION: 8 men and 16 women can do a work in 8 days.40 men and 48 women can do the same work in 2 days.how many days are required for 6 men and 12 women to do the same work.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 8 men and 16 women can do a work in 8 days.40 men and 48 women can do the same work in 2 days.how many days are required for 6 men and 12 women to do the same work.      Log On


   

Question 917391: 8 men and 16 women can do a work in 8 days.40 men and 48 women can do the same work in 2 days.how many days are required for 6 men and 12 women to do the same work.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = how many days 1 man could do the work if alone;
let w = how many ways 1 woman could do the same work alone.

cross%28%288%281%2Fm%29%2B16%281%2Fw%29%2940=1%29 and cross%28%2840%281%2Fm%29%2B48%281%2Fw%29%292=1%29

Two equations, two unknown variables; simplify each equation and solve the system.

The first arrangement of workers
%288%2Fm%2B16%2Fw%298=1 to account for 1 job
64%2Fm%2B128%2Fw=1, and LCD is mw
64w%2B128m=mw

Second arrangement of workers
%2840%2Fm%2B48%2Fw%292=1
80%2Fm%2B96%2Fw=1
80w%2B96m=mw

Two equal formulas for mw.
64w%2B128m=80w%2B96m
32m=16w
2m=w
This is the relationship between m and w, which through substitution,
allows to find through either of the mw equations, to solve for w and m,
the NUMBER OF DAYS for one woman to do one job and the NUMBER OF DAYS for one man to do one job.

Use this system:
highlight_green%28system%2864w%2B128m=mw%2C90w%2B96m=mw%2Cw=2m%29%29

(Further steps, not yet done, but you need to do them.)

You can then answer the actual question from there, using RT=J for
rate time job, uniform work rates formula.

Substituting w=2m in the 64w%2B128m=mw, solving for m gives
highlight%28m=128%29 days and this means highlight%28w=256%29 days.

Now, use those to solve the question asked.


Rate in jobs per day for the 6 men and 12 women,
%286%2F128%2B12%2F256%29

Let t be the number of days for this group to do 1 job.
The uniform rates rule gives:
highlight%28%286%2F128%2B12%2F256%29t=1%29
Solve for t.
-
-
RESULT: highlight%28t=10%262%2F3%29 days.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

8 men and 16 women can do a work in 8 days.40 men and 48 women can do the same work in 2 days.how many days are required for 6 men and 12 women to do the same work.


Time 6 men and 12 women take: highlight_green%28highlight_green%2810%262%2F3%29%29 days

You can do the check!! 

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