Question 44

An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?


Let's say length of express train = $$x$$
So length of goods train = $$2x$$
Total length travelled by express train = $$3x = ((80-40) \times \frac{5}{18}) \times 54 $$ (Where $$(80-40) \times \frac{5}{18})$$ = relative velocity of express train w.r.t. goods train in meter/sec.)
So $$x =200$$ meter.
Now crossing a plateform of length 400 m., total length travelled by train = 600 m=$$t\times(80 \times \frac{5}{18})$$
$$t = 27$$ sec.

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