Answer :
Answer:
Therefore 6 men can complete 36 houses in 8 months.
Step-by-step 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.
[tex]T\propto\frac x m[/tex]
Therefore
[tex]\frac{T_1}{T_2}=\frac{x_1}{x_2}.\frac{m_2}{m_1}[/tex]
Given that,four men can build 12 houses in 4 months.
[tex]x_1[/tex]= 12, [tex]m_1[/tex]=4, [tex]T_1[/tex] = 4 months, [tex]x_2[/tex]=36, [tex]T_2[/tex] = 8 months and [tex]m_2[/tex] = ?
[tex]\frac{T_1}{T_2}=\frac{x_1}{x_2}.\frac{m_2}{m_1}[/tex]
[tex]\Rightarrow \frac{4}{8}=\frac{12}{36}.\frac{m_2}{4}[/tex]
[tex]\Rightarrow \frac 12=\frac13.\frac{m_2}{4}[/tex]
[tex]\Rightarrow \frac{m_2}{4}=\frac12\times \frac31[/tex]
[tex]\Rightarrow m_2=\frac12\times \frac31\times 4[/tex]
[tex]\Rightarrow m_2 =6[/tex]
Therefore 6 men can complete 36 houses in 8 months.