Two trains P and Q, measure 200 m and 300 m in length, respectively. The faster train, coming from behind, takes 48 seconds to overtake the slower when moving in the same direction. When they approach each other from opposite directions, they cross each other completely in 20 seconds. Determine the speed of the faster train.
63.75 km/h
Combined length of both trains: \(200+300=500\) m \(=0.5\) km.
Same direction (overtaking): relative speed \(=(u-v)\), and \((u-v)\times\tfrac{48}{3600}=0.5 \Rightarrow u-v=37.5\) km/h.
Opposite directions (crossing): relative speed \(=(u+v)\), and \((u+v)\times\tfrac{20}{3600}=0.5 \Rightarrow u+v=90\) km/h.
Adding the two equations: \(2u=127.5 \Rightarrow u=63.75\) km/h.
Hence, the speed of the faster train is 63.75 km/h.
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