Two men and six boys can cut a field in 3hours. If the men work at 3/2 times that of the boys, how many men are required to cut the field in 2hrs.

let a man's rate be x fields/h

let a boy's rate be y fields/h

so 2/x + 6/y = 1/3
times 3xy
6y + 18x = xy
6y - xy = -18x
y = -18x/(6-x) = 18x/(x-6) , x > 6

also given: x = (2/3)y

then x = (2/3)(18x)/(x-6)
x(x-6) = 12x
x^2 - 18x =
x(x-18) = 0
x = 18 (or x = 0, which we reject)
then 18 = (2/3)y
y = 27

Man's rate = 1/18 fields per hour
boy's rate = 1/27 fields per hour

So one man can cut the field in 18 hrs
so 9 men can cut the field in 2 hrs

is there any formula one can use to solve this problem ? becauze I have a straight formula forrit

Reiny is wrong

To solve this problem, we can start by determining the work rate of each person. Let's assume that the work rate of one boy is 'B' and the work rate of one man is 'M.'

According to the given information, it takes two men and six boys working together to cut the field in 3 hours. So, their combined work rate is:

2M + 6B = 1/3 (since they complete 1 whole field in 3 hours)

It is also given that the work rate of one man is 3/2 times that of one boy. Therefore, we can write:

M = (3/2)B

Now, we can substitute this expression for M into the first equation:

2(3/2)B + 6B = 1/3

Simplifying this equation gives us:

3B + 6B = 1/3
9B = 1/3
B = 1/27

We have found the work rate of one boy to be 1/27. Now we need to find the work rate of one man using the second equation:

M = (3/2)B
M = (3/2)(1/27)
M = 1/18

This means that one man can cut 1/18th of the field in one hour.

To determine how many men are required to cut the field in 2 hours, we divide the work done by one man in one hour by 2:

(1/18)/2 = 1/36

Therefore, it would take 36 men working together to cut the field in 2 hours.