Let v(mph) ,t(h) be John's velocity and the time the trip took, then vt is the distance between 2 houses

\(\left\{{}\begin{matrix}\left(v-10\right)\left(t+2\right)=vt\\\left(v+20\right)\left(t-2\right)=vt\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}vt+2v-10t-20=vt\\vt-2v+20t-40=vt\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}2v-10t-20=0\\2v-20t+40=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}v=5t+10\\10t-60=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}v=40\\t=6\end{matrix}\right.\)

The answer is : 40 x 6 = 240 (mi)