The train roars through the station. A waiting passenger times its transit past the point where she stands. It takes seconds. To pass the whole station requires seconds from the time the engine enters the station until the time the last car exits it. (The passenger didn't know this, but we do.) The platform is meters long.
How long is the train and what is its speed?
Solution
In the figure below, P is the location of the passenger; S and E are the start and end (respectively) of the station platform.
Now, it took seconds from the moment when the front of the train reached S to the moment when the rear of the train passed E. We also know that it took seconds from the moment when the front of the train passed P to the moment when the rear of the train passed P. Naturally that seconds applies to any other point on the platform, say S. So it took seconds for the back of the train to travel the meters of the platform. Ha! The speed of the train is .
If it takes seconds for the whole train to pass a point while going m/s, then the train is m long.
If you convert this speed to kilometers or miles per hour, you'll see that it's not a particularly fast train. But it still roared.
