Train or Walk

Chefland has all the cities on a straight line. There are $N$ cities in Chefland numbered $1$ to $N$. City $i$ is located at coordinate $x_i$ on the x-axis. Guru wants to travel from city $A$ to city $B$. He starts at time t=0. He has following choices to travel. 1. He can walk $1$ metre in $P$ secs. 2. There is a train that travels from city $C$ to city $D$ which travels $1$ metre in $Q$ secs wh