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(B) Let the length of each train be $x \, m$.The speed of the first train is $v_1 = \frac{x}{4} \, m/s$.The speed of the second train is $v_2 = \frac{

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$\frac{40}{9}$

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(B) Let the length of each train be $x \, m$.The speed of the first train is $v_1 = \frac{x}{4} \, m/s$.The speed of the second train is $v_2 = \frac{x}{5} \, m/s$.When the trains move in opposite directions,their relative speed is $v_{rel} = v_1 + v_2 = \frac{x}{4} + \frac{x}{5} = \frac{5x + 4x}{20} = \frac{9x}{20} \, m/s$.To cross each other,the total distance to be covered is the sum of their lengths,which is $x + x = 2x \, m$.The time taken to cross each other is $t = \frac{	ext{Total Distance}}{	ext{Relative Speed}} = \frac{2x}{9x/20} = 2x 	imes \frac{20}{9x} = \frac{40}{9} \, seconds$.

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be:

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