How Do You Calculate Train Velocities When Moving in Opposite Directions?

[psykatic]

Homework Statement

Two trains A and B, 125m and 100m long respectively are moving in opposite directions on parallel tracks. the velocity of the train B is three times that of train A. The train takes 4s to pass each other, calculate the velocity of each train?

Homework Equations

Velocity=$$\frac {Distance}{Time}$$

The Attempt at a Solution

Let the velocity of train A be 'v', hence the velocity of the train B would be '3v'.

The relative velocity of train A w.r.t train B = $$v_A- v_B$$
=v-(-3v)=4v

The distance to be covered= 125+100= 225m

Velocity=$$\frac{Distance}{Time}$$

Hence, velocity, 4v= $$\frac{225}{4}$$
Therefore, 16v=225

Thus, v=14.1

Hence, $$v_A$$=14.1 m/s and $$v_B$$= 42.3 m/sI've reached the final answer, by using the textual methodology. But the thing which is bothering me is the distance covered, which is given by the addition of the length of both the trains (statement highlighted). Please explain me as to why do we add these lenghts, when the entire train (considering it as a whole, either A or B) moves across the length of the other, and not its own!

 

[Focus]

Get two trains and try it...

The moment before they start passing each other:

Train 1 ------------------ Train 2 (total distance = sum of distances)
_______________/////////////////////////
////////////////////// ________________

The moment after they have passed each other:

Train2 ------------------ Train 1

//////////////////////// __________________
________________////////////////////////////


Notice (look at the tails) that each train has to travel its own length, and the other trains length. Hope this helps :)

 

[psykatic]

oh, yes! got it! actually i was considering one train, and observing it going past the others!