A man sitting in a train travelling at the rate of $50$ km/hr observes that it takes $9$ sec for a goods train travelling in the opposite direction to pass him. If the goods train is $187.5$ m long, find its speed?

The man's speed is $50$ km/hr, which is $50 \times (5/18) = 125/9$ m/s. Let the goods train's speed be $v$ m/s. Since they travel in opposite directions, their relative speed is $(125/9 + v)$. The goods train passes the man in 9 seconds, covering its own length of 187.5 m, so the relative speed is also $187.5 / 9 = 125/6$ m/s. Equating the two gives $125/9 + v = 125/6$, so $v = 125/18$ m/s. Converting this back to km/hr by multiplying by $18/5$, the goods train's speed is $25$ km/hr.

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