Everything Is Proportional

Just imagine that each of the three men builds one of the three houses. They all stop and start at the same time, and so...

One man takes the same time to build one house as three men take to build three houses!

Let each man have the same building speed $s$ measured in $\text{houses/month}$ .

Let's find the value of $s$ .
Since men build together $3$ houses in $3$ months, their combined speed is $1 \ \text{house/month}$ , which makes $s$ be a third of it, so $s = \dfrac13$ .

Since $s=\dfrac13$ , we know that it takes $3 \ \text{months}$ for $1$ man to build $1$ house.

Hence, the answer is $\boxed{3 \ \text{months}}$ .

nice logic.

Here it mention that 3 men build 3 houses in 3 months. means only one man build 1 house in 3 month. anyone can misconcept by 3 mens are individually takes partly 1 month but you should know months cannot discribe the real work ability for each man. instead 1 man build one house takes 3 months.

This type of problem drove me nuts when I was young. Just remember it's parallel processes, all independent. When X entities do X tasks in Z time it's really just one doing one task in z time, and there's X of them. So, when 100 machines make 100 widgets in 1 minute it takes 1 minute for X machines to make X widgets. Drove me nuts.