Question

8 men and 16 women can do a work in 8 days 40 men and 48 women can do it in 2 days how many days 6 men and 12 women do the same work

Answer 1

Answer:

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.