Two trains travel in opposite directions at 36 km/h and 45 km/h respectively. A man sitting in slower train passes the faster train in 8 seconds. The length of the faster train isa)80 mb)120 mc)160 md)180 mCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Solution:

Let the length of the faster train be L.

Relative speed of the trains = (36 + 45) km/h = 81 km/h = 81 × 5/18 m/s = 45/2 m/s

Time taken by the faster train to cross the slower train = 8 s

Distance covered by the faster train in 8 s = (45/2) × 8 = 180 m

Therefore, L + length of the slower train = 180

Let the length of the slower train be S.

Then, L + S = 180 ----(1)

Relative speed of the trains = 81 km/h = 81 × 5/18 m/s = 45/2 m/s

Time taken by the faster train to cross the slower train = S/[(45/2)] = 2S/45 s

Distance covered by the faster train in 2S/45 s = L + S

Therefore, (45/2) × (2S/45) = L + S

Solving this equation, we get L = 180 m

Therefore, the length of the faster train is 180 m.

Answer: (d) 180 m

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