Question

Distance between Surat and Ahmedabad is 300 km two trains set off simultaneously towards each other with speed of 60km/h and 40km/h respectively. when will they cross each other
A) 3 hours
B) 15 hours
C) $\dfrac{1}{3}$ hours
D) $\dfrac{4}{3}$ hours

Answer 1

Hint
Here. We will use the formula As, two trains are 300km apart, let one train at x distance then another train will be at 300-x distance and they are moving with 60km/h and 40km/h respectively. So, by using the above formula we will get two equations at time t. then we will add both equations and then we will get the value of time at which they cross each other.

Complete step by step answer
As the two trains are set off from Surat and Ahmedabad. And the distance between Surat and Ahmedabad is 300km. These trains are moving towards each other at the speed of 60km/h and 40km/h respectively.
So, let the two trains cross each other.
Let, at time t the train which is set off from Surat travels x meter distance. Therefore, at time t the train from Ahmedabad is at distance 300-x meter.
As we know that $speed = \dfrac{{dis\tan ce}}{{time}}$ then $dis\tan ce = speed \times time$
As, Surat train is at distance x meter at time t and moving with speed 60km/h, on substituting the values in above formula, we get
$ \Rightarrow x = 60 \times t$ …………………… (1)
Similarly, Ahmedabad train is at distance 300-x meter at time t and moving with velocity 40km/h, again on substituting the values in above formula, we get
$ \Rightarrow 300 - x = 40 \times t$ …………………….. (2)
Now, in order to find the time at which both trains crossed each other. For this adding the equation (1) and equation (2), we get
$ \Rightarrow 300 - x + x = 40t + 60t$
$ \Rightarrow 300 = 100t$
$ \Rightarrow t = \dfrac{{300}}{{100}} = 3hours$
Hence, both trains will cross each other at 3 hours.
Therefore, option (A) is correct.

Note
In this question, the time taken for both the trains to cross each other is the same. Even though speed is different, time taken by the trains will be different. Students may get confused like, velocity is different therefore, time must be different, but this is not always true. If the speed of the body is greater than next then might be the distance covered by the first body will be more but time taken to reach at a point where both bodies will cross will be the same.