# Relative speed : Two trains crossing each other

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## Main Question or Discussion Point

Two trains having lengths of 120 m and 100 m are running in the opposite directions with velocities 40 km/h and 50 km/h . In what time they will completely cross each other? In the solution it's given that
Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
I fail to understand the above formula . How are the lengths of trains relevant?

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A.T.
How are the lengths of trains relevant?
You don't understand why the length of a train is relevant to how long it takes it to pass something?

gracy
Should not the question mention what their (the two train's) initial separation was?

davenn
Gold Member
2019 Award
Should not the question mention what their (the two train's) initial separation was?
it's not relevant as the timing of the crossing only involves the period that it takes to cross ( pass ) each other. it doesn't matter if they started 10 or 100 km apart
draw a pic looking down on the 2 trains as they start to cross and one below it when they finish the passing

you didn't answer AT's query as to why the length of each train is important

gracy
A.T.
Should not the question mention what their (the two train's) initial separation was?
It should, along with some other irrelevant info, to train the student's filtering skills.

DrClaude and Dale
A.T.
So how far are the ends apart, when the fronts meet? And how fast is that distance reducing?

gracy
So how far are the ends apart, when the fronts meet?
Equal to sum of the two train's lengths
And how fast is that distance reducing?
I don't know how to answer this.

And how fast is that distance reducing?
I think it is same as asking time taken by trains to cross each other

A similar type of problem I have come across is as follows
Two train each of length 100 m are running on parallel tracks. One overtakes the other in 20 seconds and one crosses the other in 10 second. Calculate the velocities of two trains. I just want to ask what's the difference between overtaking and crossing?

A.T.
I think it is same as asking time taken by trains to cross each other
No, closing speed is not the same as duration.

A.T.
I just want to ask what's the difference between overtaking and crossing?
Direction.

Direction.
Could you please explain a bit more?

Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
I fail to understand the above formula .
Time = distance/ speed
Time taken by the two trains to cross each other = distance to cross/ relative speed (as both are moving)
Distance to cross =sum of length of trains
Therefore
Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
Right?

A.T.
Time = distance/ speed
Time taken by the two trains to cross each other = distance to cross/ relative speed (as both are moving)
Distance to cross =sum of length of trains
Therefore
Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains
Right?
Yes.

gracy

Staff Emeritus
2019 Award
Gracy, I don't think PhysicsForums is helping you. You've asked us about various topics in the past, and now it's clear you haven't learned them.

The problem is that you immediately jump to asking a question here without having put much work into it, and when you are guided by someone towards the answer, you don't try and work it out for yourself, but instead ask for another hint. And another. And another. Eventually, you have been hinted all the way to the answer. Well, you've gotten the answer, but you haven't really learned.

You're going to have to decide if you want to learn or not. If you want to learn, you are going to have to spend more time thinking and working on your own. Actually, I think you have decided - you've decided that so long as you have access to PF, you don't need to learn: you can count on people hinting you all the way to an answer.

cnh1995
Homework Helper
Gold Member