Question

A train 100 M long travelling at 40 km per hour and pass overtakes another train travelling in the same direction at 30 km per hour and passes it completely in 126 Second find the length of the second train

Answer 1

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please refer the attachment

Relative velocity of train B w.r.t A is

$(Velocity)_{A}=40m/s i \\(Velocity)_{B}=-30m/s i\\ Relative \:Velocity =40i-(-30)i=70i$

hence train B appears to be at rest as seen from train A Hence

$time\: taken\: by \:train \\A \:to\: cross\: B =\frac{100+x}{70}$since Train A will only Be said to Cross B if it has Crossed the last Ciach of Train also

but time taken is 126 sec

Hence $126=\frac{100+x}{70}\\126\times70=8820=100+x\\</p><p><strong>x</strong><strong>=</strong><strong>8</strong><strong>8</strong><strong>2</strong><strong>0</strong><strong>-</strong><strong>1</strong><strong>0</strong><strong>0</strong><strong>=</strong><strong>8</strong><strong>7</strong><strong>2</strong><strong>0</strong><strong>m</strong><strong> </strong>$

hope it helps