If 15 men or 24 women or 36 boys can do a piece of work in 12 days, working 8 hours a day, how many men must be associated with 12 women and 6 boys to do another piece of work 9/4 times as great in 30 days working 6 hours a day?
Convert the rates to work/mandays or work/womandays, etc.
So rate1=job/12*15*8 manhours
rate2=job/12*24*8 femalehours
rate2=job/12*36*8 boyhours.
Finally, the equation is
9/4 job = Xmen*6hrs/day*30days*rate1+ 12women*30days*6hrs/day*rate2 + 6 boys*30days*6hrs/day *rate3
solve for Xmen.
To solve this problem, we need to find the relative efficiency of the different groups of workers and then calculate how many men should be associated with 12 women and 6 boys to complete the given piece of work in the specified time.
Let's start by finding the efficiency of each group of workers. We can calculate this by dividing the total work by the number of days, number of hours, and the number of people in each group.
So, the efficiency of 15 men can be calculated as follows:
Work done by 15 men in 12 days = 1
Work done per day by 15 men = 1/12
Work done per hour by 15 men = 1/12 ÷ 8 = 1/96
Similarly, the efficiency of 24 women can be calculated as:
Work done per hour by 24 women = 1/24 ÷ 8 = 1/192
And the efficiency of 36 boys can be calculated as:
Work done per hour by 36 boys = 1/36 ÷ 8 = 1/288
Now, we need to determine how many men, women, and boys would be required to do the work in the given time. Let's assume we need "x" men, "y" women, and "z" boys to complete the work.
Since the work has to be 9/4 times as great as the previous piece of work:
Work done in 30 days = 1 * (9/4)
Work done per day by (x) men, (y) women, and (z) boys = (9/4) ÷ 30 = 3/40
We already know the efficiencies per hour of men, women, and boys. So, we can set up the following equation based on the work done per day:
(x/96) + (y/192) + (z/288) = (3/40)
Now we need to find the values of (x), (y), and (z) to satisfy this equation.
Lastly, we have the condition that (x) men should be associated with 12 women and 6 boys. So we can set up another equation using this information:
x = 12 + 2(6)
Simplifying this equation will give us the value of (x).
By solving these two equations simultaneously, we can find the values of (x), (y), and (z), which will tell us how many men, women, and boys are needed to complete the work.