Question

A 415 m long train is running at 63 km/hr. In how much time will it cross a tunnel 285 m long?

Answer 1

Train Length=415 m

Speed=63 km/h

Tunnel Length=285 m

Now firstly Convert Speed in m/s

Then 63×5/18

=35/2 m/s

Speed=35/2 m/s

Now Find Time to cross tunnel.

Time=Distance/Speed

Now We know Train is 415 Long

See at this what will happen The Front train Will cross But entire back will be in Tunnel.We have to time for total crossing of train .

Then Distance=415+285

=700 m

Speed=35/2 seconds

So,

Time=700/35/2

=700/35×2

=40 seconds

Time➡️40 seconds

Answer 2

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

Given,

Length of the train = $415\: m$
Speed of the train = $63\: kmph$
Length of the tunnel = $285\: m$
Time taken by train to cross the tunnel = $?\: sec$



$\underline{\LARGE{\textsf{Step-1:}}}$
Express the Speed of the train in mps

We have,
$\bigstar \mathbf{1\: kmph = \dfrac{5}{18}\: mps}$

$\implies 63\: kmph = 63\times \frac{5}{18}\: mps$

$\implies Speed\: of\: the\: train = \frac{35}{2}\: mps$ ————[1]



$\underline{\huge{\textsf{Step-2:}}}$
Find the Distance covered by the train

Distance covered by the train is sum of Lengths of the train and the tunnel.

$\implies \textsf{Distance covered = Length of the train + Length of the tunnel}$

$\implies Distance\: covered = 415\: m + 285\: m$

$\implies Distance\: covered = 700\: m$ ————[2]



$\underline{\huge{\textsf{Step-3:}}}$
Find the time taken by the train to cross the tunnel.

We have,
$\bigstar \mathbf{Speed = \dfrac{Distance\: covered}{time\: taken}}$

$\implies time\: taken = \dfrac{Distance\: covered}{Speed}$

$\implies time\: taken = \dfrac{700}{\frac{35}{2}}$

$\implies time\: taken = \dfrac{1400}{35}$

$\implies time\: taken = 40\: s$

$\therefore$
$\blacksquare\: \textsf{Time taken by the train to cross the tunnel = \large{\textbf{40\: sec}}}$