Discussion

A train crosses a platform 250 m long in 30 seconds and a signal pole in 15 seconds. What is the length of the train ?

Answer: B

Correct answer: 250 m

Let the length be \(L\) and the speed \(v\). Passing the pole covers \(L\), and passing the platform covers \(L + 250\).

\[\frac{L}{v} = 15, \qquad \frac{L + 250}{v} = 30\]

Subtracting, \(\tfrac{250}{v} = 15\), so \(v = \tfrac{50}{3}\) m/s and \(L = 15 \times \tfrac{50}{3} = 250\) m.

The extra 15 seconds is exactly the time to cover the platform alone.

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