Question

The number of hours that is takes men to build x houses varies directly as the number of houses and inversely as the number of men. If four men can build 12 houses in 4 months, how many men are needed to assemble 36 houses in 8 months?

Answer 1

Therefore 6 men can complete 36 houses in 8 months.

Explanation:

Given that, the number of hours that is takes men to build x houses varies directly as the number of house and inversely as the number of men.

`T\propto\frac x m`

Therefore

`(T_1)/(T_2)=(x_1)/(x_2).(m_2)/(m_1)`

Given that,four men can build 12 houses in 4 months.

`x_1`= 12,
`m_1`=4,
`T_1` = 4 months,
`x_2`=36,
`T_2` = 8 months and
`m_2` = ?

`(T_1)/(T_2)=(x_1)/(x_2).(m_2)/(m_1)`

`\Rightarrow (4)/(8)=(12)/(36).(m_2)/(4)`

`\Rightarrow \frac 12=\frac13.(m_2)/(4)`

`\Rightarrow (m_2)/(4)=\frac12* \frac31`

`\Rightarrow m_2=\frac12* \frac31* 4`

`\Rightarrow m_2 =6`

Therefore 6 men can complete 36 houses in 8 months.