Suppose that $3$ people require $3$ hours to complete $3$ houses. Assume that they work independently. How much time is required for $7$ people to complete $7$ houses?
I try to apply variation technique to solve the problem, i.e. determine relationship among quantities (people, houses and time). But I couldn't formulate an equation to solve the questions.
Any hint would be much appreciated.
On
One thing you can remember is $\frac{\text{LABOR}\times\text{TIME}}{\text{JOBS}}$ stays constant. Because $\text{LABOR}\times\text{TIME}$ is the work done and work per job doesn't change. Thus $$\frac{\text{LABOR}_1\times\text{TIME}_1}{\text{JOBS}_1}=\frac{\text{LABOR}_2\times\text{TIME}_2}{\text{JOBS}_2}$$ and in this case $$\frac{3\times3}{3}=\frac{7\times x}{7}$$
Let $t$ the time a single person needs to build one house. So, the power of a single person is $P=\frac{1}{t}$. From the initial data we have: $$ 3\cdot\frac{1}{t}=\frac{3}{3}=1\Rightarrow t=3 h $$ Now if $x$ is the time needed by the $7$ people to build $7$ houses, we get: $$ 7\cdot\frac{1}{3}=\frac{7}{x}\Rightarrow x=3h $$ P.S.: There are two implicit assumptions here: (a). Each persons work at the same rate (power) with everybody else, (b). Power is "additive", in the sense that: $ \ \frac{W_A}{t_A}+\frac{W_B}{t_B}=\frac{W_{AB}}{t_{AB}}$