Two men and six boys can cut a field in 3 hours. If the men work at 3/2 times that of the boys, how many men are required to cut the field in 2hours?
2/m + 6/b = 1/3
1/m = (3/2)/b
m = 18. That means one man can cut the field in 18 hours
2 men can do it in 9 hours
oops. I meant 9 men can do it in 2 hours.
you have to ask yourself. If a man can do the job in m hours, how much can he do in one hour? 1/m
So, 2 men can do 2/m of the job in one hour.
Same for the 6 boys.
So, since they all can complete the job in 3 hours, in one hour they have done 1/3 of the job.
You have to think of things in this way -- adding up all the work done by each person gets some fraction of the job done in an hour. Now go back and look at the equations. Oh, yeah -- and read the section in your text where this is covered.
thanks man.. but why is it 2/m +6/b=1/3 and not 2m+6b=3
thanks... but i still don't understand how got the equation. pls can you help me out?
To solve this problem, we need to determine the work rate of each man and boy and then determine how many men are needed to cut the field in 2 hours.
Let's start by assigning variables:
Let's assume the work rate of each boy is "b" and the work rate of each man is "m."
We are given that two men and six boys can cut the field in 3 hours. So, the total work done is 1 field.
The total work done by two men and six boys in 3 hours is:
(2m + 6b) * 3 = 1
Next, we are given that the men work at 3/2 times that of the boys, which means their work rate ratio is 3:2.
We can express the men's work rate in terms of the boys' work rate:
m = (3/2)b
Substituting this value in the equation, we can solve for b:
(2 * (3/2)b + 6b) * 3 = 1
(3b + 6b) * 3 = 1
9b * 3 = 1
27b = 1
b = 1/27
Now, we know the work rate of each boy is 1/27.
To find the work rate of each man, we can substitute the value of b back into the men's work rate equation:
m = (3/2) * (1/27) = 1/18
We need to determine how many men are required to cut the field in 2 hours.
Let's assume the number of men required is "x."
The total work done by x men and 6 boys in 2 hours is
(xm + 6b) * 2 = 1
Substituting the values of m and b:
((1/18) * x + (1/27) * 6) * 2 = 1
(x/18 + 2/9) * 2 = 1
(x/18 + 4/9) = 1/2
x/18 = 1/2 - 4/9
x/18 = 9/18 - 8/18
x/18 = 1/18
x = 1
Hence, only one man is required to cut the field in 2 hours.