A man sitting in a train which is traveling at 40 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 270 m long, find its speed.
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Relative speed of trains moving in opposite directions is the sum of their speeds.
The goods train covers its own length of $270$ m relative to the man in $9$ seconds. Relative speed $= \dfrac{270}{9}$ m/s $= 30$ m/s. Multiply by $18/5$ to convert m/s into km/h: $30 \times \dfrac{18}{5} = 108$ km/h. Since the man's train and the goods train move toward each other, this relative speed equals the sum of the two speeds: $40 + v = 108$. \[\boxed{v = 68 \text{ km/h}}\]