Aptitude - Problems on Trains - Discussion

Based on the below formula -- >

If two trains of length a(i.e. 27x) metres and b(i.e. 17y) metres are moving in opposite directions at x m/s and y m/s, then:

The time taken by the trains to cross each other (i.e.23 sec) =

(27x + 17y)
```````` secs
(x + y)


Therefore, the above solution is provided based on this derivation. Its given in the formulas section.

very good solution....

It's correct method to solve this problem.

(27x+17y)/x+y=23 how did used that step?

Anyone please help me how this x+y is divided.

I can't get this step

(27x+17y) / (x+y) = 23

Why we have to use this? can any one explain me.

Let me explain in detail if anyone still not understood yet.

Please remember the formula for finding speed. Speed = Distance/Time.
Therefore, Distance = Speed x Time.

If a train crosses a man/pole/post/tree in T seconds, and speed of the train is S m/s, then

Then, the Length of the Train = (Speed x Time) = ST metres.

Note: Here, the distance traveled by train in T seconds at the Speed of S m/s is equal to the length of the train.

Now, lets come to the given problem.

Let speed of the first train = X.
Time taken taken by the first train to cross a man = 27 seconds.
Therefore, Length of the first train = Speed x Time = X x 27 = 27X metres.

Let speed of the second train = Y.
Time taken taken by the second train to cross a man = 17 seconds.
Therefore, Length of the second train = 17Y metres.

Important Formula:
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
The time taken by the trains to cross each other = (a + b) / (u + v) sec.

Given that, (a + b) / (u + v) = 23 seconds.

Here, a = 27X, b = 17Y and u = X, v = Y.

Therefore, (27X + 17Y)/(X + Y) = 23.

=> 27X + 17Y = 23X + 23Y

=> 4X = 6Y

=> X/Y = 6/4 = 3/2

=> X : Y = 3 : 2.