Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is
Explanation:
Let the length of the smaller train be L meters. Also, let the speeds of faster and slower trains be ‘f’ and ‘s’ m/s.
Given, f - s = 6 × 5/18 = 5/3 m/s ⇒ f = s + 5/3 …(1)
Faster train crosses a lamp post in 12 seconds. ∴ 160/f = 12 ⇒ f = 40/3
∴ s = f – 5/3 = 35/3
The two trains cross each other in 14 seconds. ∴ (160 + L)/(f + s) = 14 ⇒ L = 14(f + s) – 160 ⇒ L = 14 × 25 – 160 ⇒ L = 350 – 160 = 190
Hence, option (c).
Concept: Trains
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