Question

A train $280\,m$ long is moving at a speed of \[60{\text{ }}km/h\]. What is the time taken by the train to cross a platform \[220\,m\] long?
A. \[45\,s\]
B. \[40\,s\]
C. \[35\,s\]
D. \[30\,s\]

Answer 1

Hint: In this question, we are required to find the time taken by the $280\,m$ long train to cross a \[220\,m\] long platform. Let the front tip of the train be point \[A\] and the end of the train be point \[B\].Then, the time taken by the train to cross the platform starts when point \[A\] of train touches the platform and ends when point \[B\] of the train leaves the platform.

Formulae used:
$t = \dfrac{d}{s}$
where $s$= speed of the object, $d$= distance travelled by the object and $t$= time taken by the object.

Complete step by step answer:
Given, Length of train $L1 = 280\,m$, Speed of train $S = 60\,km/h$ and Length of platform $L2 = 220\,m$. Let the front side of the train be \[A\]. Let the back side of the train be \[B\]. Let the starting point of the platform be $E$. Let the ending point of the platform be $F$ . The total time taken for the train to cross the platform will start when point \[A\] touches point \[E\] and ends when point \[B\] touches point \[F\]. Therefore, total distance $D$ to be travelled by the train
$D = BA + EF \\
\Rightarrow D = L1 + L2 \\
\Rightarrow D = 280m + 220m \\
\Rightarrow D = 500m \\ $
Speed of the train $S = 60km/h = 60 \times \dfrac{5}{{18}}m/s = \dfrac{{50}}{3}m/s$
Therefore, Time taken by the train to cross the platform
Using the formulae $t = \dfrac{d}{s}$, we get
$t = \dfrac{D}{S} \\
\Rightarrow t= \dfrac{{500m}}{{\dfrac{{50}}{3}m/s}} \\
\therefore t = 30\,s \\ $
Therefore, option (D) is the correct answer.

Note: To reduce the time taken to solve such problems in competitive exams, we directly add up the length of the train and the platform and divide it by the train’s speed.This method gives us the answer.