Question

A train $100$ meters long moving at a speed of $50$ km/hr crosses a train $120$ meters long coming from the opposite direction on parallel tracks in $6$seconds. The speed of the train is
A) $132km/hr$
B) $82km/hr$
C) $60km/hr$
D) $50km/hr$

Answer 1

Here we will use the concept of relative speed as both train are in opposite motion so the relative speed will be the sum of both the speed
We have given a train of $100$m long moving with the speed of $50$km/hr and another train of $120$m and both are crossing each other in 6s.

Formula used:
The relative speed of two trains when both are in opposite directions= speed of first train + speed of the second train.
$\text{Speed}=\dfrac{distance}{time}$

Complete step by step solution:
Here a train of 100m is crossing another train of 120m so the sum of lengths of the trains is the distance the second train travels.

$$100 + 120m{\text{ }} \\\ \Rightarrow 220m \\\ \Rightarrow 0.22km \\\$$

Now let the speed of the second train be $x$ km/h
Since they are in opposite directions.
So relative speed = $x + 50{\text{ }}km/h$
And time = $6{\text{ }}seconds{\text{ }} = {\text{ }}6/3600{\text{ }}seconds{\text{ }} = {\text{ }}1/600{\text{ }}hours$
And we know that distance=speed $\times$ time
$0.22 = \left( {x + 50} \right) \times 1/600$
Multiply both side by $600$
$\Rightarrow 0.22 \times 600{\text{ }} = x + 50$

$$\Rightarrow 132 = x + 50 \\\ \Rightarrow x = 132 - 50 \\\ \Rightarrow x = 82{\text{ }}km/h \\\$$

$\therefore$ The speed of second train is $82km/hr$

Note:
In this type of question, we need to be alert with the conversion of speed and for that, we can use trick also like if we need to convert speed from m/s to km/hr then we need to multiply with $\dfrac{18}{5}$ and if we need to convert speed from km/hr to m/s then we need to multiply with $\dfrac{5}{18}$
Example: Convert 5m/s into km/hr then $5 \times \dfrac{18}{5} = 18km/hr$.