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.

Answer 1

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

Answer 2

Reiny is wrong

Answer 3

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