Question

Travelling with a speed of 45 km/hr, a train crosses a 120 meter long bridge in
40 seconds. Find the length of the train​

Answer 1

$Speed \: of \: a \:train (s) \\= 45 \: km/hr \\= 45 \times \frac{1000\: m }{60 \times 60 \: seconds } \\= \frac{25}{2} \: m/s$

$Length \: of \: the \: bridge (l) = 120 \: m$

$Let \: length \: of \: the \: train = x \: m$

$Distance \:travelled\: to \: cross \: the \\bridge (d) = l + x \\= (120 + x ) \: m$

$Time \:taken \: to \: cross \:the \:bridge (t) = 40\:s$

/* we know that */

$\boxed{ \pink{ Speed = \frac{ Distance }{Time } }}$

$\implies \frac{25}{2} = \frac{120+x}{40}$

$\implies \frac{25}{2} \times 40 = 120 + x$

$\implies 25 \times 20 = 120 + x$

$\implies 500 = 120 + x$

$\implies 500 - 120 = x$

$\implies x = 380 \: m$

Therefore.,

$\red{ length \: of \: the \: train}\green { = 380 \: m$

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