Work together!

Botham can paint at a rate of $\dfrac{1}{20}\text{th}$ of a house per hour.

George can paint at a rate of $\dfrac{1}{30}\text{th}$ of a house per hour.

Add their efforts and they can paint $\dfrac{1}{20} + \dfrac{1}{30} = \dfrac{1}{12}\text{th}$ of a house in an hour.

So if their rate is $\dfrac{1}{12}\text{th}$ of a house per hour it will take $\color{#3D99F6}\boxed{12}$ hours to paint an entire house

In $60$ hours, Botham can paint $60/20$ or $3$ houses, and George can paint $60/3$ or $2$ houses.

Since $3+2=5$ , in $60$ hours Botham and George together can paint $5$ houses, so it takes them $12$ hours to paint $1$ house.