SOLUTION: if 2 men, 4 women and 2 boys can complete 10 hectare land in ten days then 4 men,6 women and 8 boys can complete 16 hectare land in how many days.if ratio of their efficiency men,w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: if 2 men, 4 women and 2 boys can complete 10 hectare land in ten days then 4 men,6 women and 8 boys can complete 16 hectare land in how many days.if ratio of their efficiency men,w      Log On


   

Question 785140: if 2 men, 4 women and 2 boys can complete 10 hectare land in ten days then 4 men,6 women and 8 boys can complete 16 hectare land in how many days.if ratio of their efficiency men,women and boys is 5:4:2.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
ratio of their efficiency men, women and boys is 5:4:2.
So:
%28matrix%284%2C1%2C%0D%0A1%2C+%22man%27s%22%2C+work%2C+rate%29%29%22%3A%22%28matrix%284%2C1%2C%0D%0A1%2C+%22woman%27s%22%2C+work%2C+rate%29%29%22%3A%22%28matrix%284%2C1%2C%0D%0A1%2C+%22boy%27s%22%2C+work%2C+rate%29%29  %22%22=%22%22  %225%3A4%3A2%22

A ratio can be multiplied or divided through by any positive
constant.  So we'll divide it through by 2, so that the 
smallest rate, the boy's, will correspond to 1.

That is  5 : 4 : 2 =  2.5 : 2 : 1.  

Therefore:

%28matrix%284%2C1%2C%0D%0A1%2C+%22man%27s%22%2C+work%2C+rate%29%29%22%3A%22%28matrix%284%2C1%2C%0D%0A1%2C+%22woman%27s%22%2C+work%2C+rate%29%29%22%3A%22%28matrix%284%2C1%2C%0D%0A1%2C+%22boy%27s%22%2C+work%2C+rate%29%29  %22%22=%22%22  %22%282.5%29%3A%282%29%3A%281%29%22

Suppose 1 boy's work rate is x hectares/day
Then 1 woman's work rate is 2x hectares/day
and 1 man's work rate is 2.5x hectares/day

2 men, 4 women and 2 boys can complete 10 hectare land in ten days
The combined rate of 2 men, 4 women and 2 boys = 5x+8x+2x = 
15x hectares/day

2 men's rate is 2(2.5x) hectares/day or 5x hectares/day
4 women's rate is 4(2x) hectares per day or 8x hectares/day
2 boys' rate is 2(x) hectares per day or 2x hectares per day

So their combined rate is 10 hectares/10 days or 1 hectare per
 day.

So we set the two equal:

15x = 1
  x = 1%2F15 

So 1 boy's rate is x or 1%2F15 hectares/day,
1 woman's rate is 2x or 2%2F15 hectares/day,
and 1 man's rate is 2.5x or 2.5%2F15 hectares/day.

4 men, 6 women and 8 boys can complete 16 hectare land in how many days 
Let t = how many days are required

Then in t days, 
4 men can complete 4·2.5%2F15t or 10t%2F15 hectares
6 women can complete 6·2%2F15t or 12t%2F15 hectares
8 boys can complete 8·1%2F15t or 8t%2F15 hectares.

So the sum of the hectares they have completed in t days must = 16 hectares

10t%2F15%22%22%2B%22%2212t%2F15%22%22%2B%22%228t%2F15  %22%22=%22%22  16

%2810t%2B12t%2B8t%29%2F15  %22%22=%22%22  16

%2830t%29%2F15  %22%22=%22%22  16

2t = 16
 t = 8

Answer: 8 days.

Edwin