How long is the train?

Question

A train travelling at constant speed passes a signal post (a point) in 10 seconds, measured from when the front reaches the post to when the rear clears it. The same train passes completely through a 300 metre platform in 25 seconds, from the front entering to the rear leaving.

How long is the train, and how fast is it going?

Accepted Answer

The train is 200 metres long and travels at 20 metres per second (72 km/h). Passing the post. From the moment the front reaches the post until the rear passes it, the train moves a distance equal to its own length L. So L = v × 10, where v is the speed. Passing the platform. From the front entering to the rear leaving, the train moves L + 300. So L + 300 = v × 25. Solve. Subtract: 300 = 15v, so v = 20 m/s. Then L = 10 × 20 = 200 m. Check. Passing the platform: 200 + 300 = 500 m at 20 m/s takes 25 s. Correct. The general trick. Every "passing" problem is about how far the front of the train tr…

How long is the train?

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