SOLUTION: 12 men can complete a work in ten days. 20 women can complete the same work in twelve days. 8 men and 4 women started working and after nine days 10 more women joined them. How ma

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 12 men can complete a work in ten days. 20 women can complete the same work in twelve days. 8 men and 4 women started working and after nine days 10 more women joined them. How ma      Log On


   

Question 983773: 12 men can complete a work in ten days. 20 women can complete the same work in twelve days. 8 men
and 4 women started working and after nine days 10 more women joined them. How many days will they
now take to complete the remaining work?
Found 3 solutions by solver91311, josgarithmetic, MathTherapy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If 12 men can do a job in 10 days, then 12 men can do of the job in 1 day, and then 1 man can do of the job in 1 day. Similarly, 1 woman can do of the job in 1 day.

So 8 men and 4 women working for 9 days do of the job, leaving of the job for 8 men and 14 women to accomplish in days, so:



Solve for

John

My calculator said it, I believe it, that settles it

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
R rate of 1 man
r rate of 1 woman
system%2812R%2A10=1%2C20r%2A12=1%29
-
system%28R=1%2F120%2Cr=1%2F240%29

Let t be the time needed to complete after some of the job was done using the described combination of men and women.

8%281%2F120%29%2A10%2B4%281%2F240%29%2A10%2B8%281%2F120%29t%2B%284%2B10%29%281%2F240%29t=1
Simplify this and solve for t.

80%2F120%2B40%2F240%2B8t%2F120%2B14t%2F240=1

8%2F12%2B4%2F24%2B%288%2F120%29t%2B%287%2F120%29t=1
2%2F3%2B1%2F6%2B%282%2F30%29t%2B%287%2F120%29t=1
LCD is 120.
Multiply LCD by both sides.
80%2B20%2B8t%2B7t=120
15t=120-80-20
15t=20
t=20%2F15
highlight%28t=4%2F3=1%261%2F3%29, this many days.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

12 men can complete a work in ten days. 20 women can complete the same work in twelve days. 8 men
and 4 women started working and after nine days 10 more women joined them. How many days will they
now take to complete the remaining work?
Time taken by 8 men and 14 women to do remaining 1%2F4 of work: highlight_green%282%29 days