Question

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

Answer 1

We will need to translate this to equations, first.

Let x be the fraction of the filed one man cuts in 1 hour.

Let y be the fraction of the filed one boy cuts in 1 hour.

Now, if we have 2 men, they will cut 2x of the filed in 1 hour, and 6x of the field in 3 hours.

And if we have 6 boys, they will cut 6y of the filed in 1 hours, and 18y of the field in 3 hours.

If 2 men and 6 boys cut the whole field in 3 hours, the sum of these quantities have to be 1 field, thus, we have the equation:

`6x+18y=1`

If the men work 3/2 times of the boys, this means that the cut 3/2 more than the boys in 1 hour.

That is, x is 3/2 times y:

`x=(3)/(2)y`

With this, we can substitute x into the first equation:

`\begin{gathered} 6x+18y=1 \\ 6\cdot(3)/(2)y+18y=1 \\ (18)/(2)y+18y=1 \\ 9y+18y=1 \\ 27y=1 \\ y=(1)/(27) \end{gathered}`

And now, we can use this into the second equation to find out x:

`\begin{gathered} x=(3)/(2)y \\ x=(3)/(2)\cdot(1)/(27) \\ x=(3)/(54) \\ x=(1)/(18) \end{gathered}`

Thus, 1 man cuts 1/18 of the field in 1 hour. In two hours, he cuts twice as much, so he cuts 2/18 which is the same as 1/9.

If we need 1 man to cut 1/9 of the field in 2 hours, we will need 9 men to cut the whole field in 2 hours.

Thus, 9 men are required to cut the field in 2 hours.