Question 29
(USA 3) A number of signal lights are equally spaced along a one-way railroad track, labeled in order $1,2,\ldots,N$ $(N\ge2)$. As a safety rule, a train is not allowed to pass a signal if any other train is in motion on the length of track between it and the following signal. However, there is no limit to the number of trains that can be parked motionless at a signal, one behind the other. (Assume that the trains have zero length.)
A series of $K$ freight trains must be driven from Signal $1$ to Signal $N$. Each train travels at a distinct but constant speed (i.e., the speed is fixed and different from that of each of the other trains) at all times when it is not blocked by the safety rule. Show that regardless of the order in which the trains are arranged, the same time will elapse between the first train’s departure from Signal $1$ and the last train’s arrival at Signal $N$.
A series of $K$ freight trains must be driven from Signal $1$ to Signal $N$. Each train travels at a distinct but constant speed (i.e., the speed is fixed and different from that of each of the other trains) at all times when it is not blocked by the safety rule. Show that regardless of the order in which the trains are arranged, the same time will elapse between the first train’s departure from Signal $1$ and the last train’s arrival at Signal $N$.