Question

A train passes a telegraph post in 8 seconds and a 264 m long bridge in 20 seconds. What is the length of the train?

Answer 1

Hint: In the above question we need to find the length of the train, So, we will assume the length of the train be ‘x’. It is given that a train passes a telegraph post in 8 seconds.
We can form an equation from this given information by using formula
Speed = $\dfrac{{{\text{distance}}}}{{{\text{time}}}}$.
In the same way we will form a second equation by using the length of a bridge that is 264 m and the time taken to pass this bridge is 20 seconds.

Complete step by step answer:
According to the question;
Let the length of the train be $x$ meters
A train passes a telegraph post in $8$ seconds.
Using formula, Speed = $\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
$ \Rightarrow $Speed = $\dfrac{x}{8}$m/sec
A train passes through a bridge whose length = 264 m
Time taken to pass this bridge = 20 seconds
Total distance = $264$ + length of the train
(length of a train is also included in Total distance because a train is not a point object like a car or a bus, its length is too large so we cannot ignore the length of a train as it covers some distance also.)
$\Rightarrow $ Total distance = (264 + x) m
Using formula, Speed = $\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
$ \Rightarrow $ Speed = $\dfrac{{264 + x}}{{20}}$m/sec
Now, equating both the value of speed, we get;
$ \Rightarrow \dfrac{x}{8}$= $\dfrac{{264 + x}}{{20}}$
Cross multiplying, we get;
$ \Rightarrow 20x = 8(264 + x)$
On simplification,
$ \Rightarrow 20x = (264 \times 8) + 8x$
On further simplification,
$ \Rightarrow x = \dfrac{{264 \times 8}}{{12}} $
$\Rightarrow x= 176$m

Thus, the length of the train is 176 m.

Note:
In this question you might think that why we added the length of a train with the length of a bridge to find the value of distance covered and we also used the length of a train in place of distance when train was crossing a telegraph post this is because the size of a train is large in comparison to cars or other objects that is why we can’t ignore the length of a train, So we have to take the length of a train while calculating the distance. But we ignore the length of a car or any other object because we consider them as point objects.