Solving the Train Length Ratio Puzzle

[renegade05]

Homework Statement

Two trains, A and B, are moving towards each other with relative speed 0.8c. The
passing of the two trains (from when their fronts align to when their backs align) takes 20%
longer as observed from train A as is does as observed from train B. What is the ratio of the
length of A to the length of B?

Homework Equations

I am guessing:
T'=Tsqrt(1-(v/c)^2)
L'=Lsqrt(1-(v/c)^2)

The Attempt at a Solution

I am confused, I feel like there is missing information?

I am trying to relate these two equations! but I am really not sure how to go about solving this one! please help. just so i know where to start...

 

[Chestermiller]

Let L_A represent the length of train A in its own rest frame, and let L_B represent the length of train B in its own rest frame. Let v be the relative velocity.

The observers on train A focus on 3 sequential events:
1. The front of train B aligns with the front of train A.
2. The front of train B aligns with the rear of train A.
3. The rear of train B aligns with the rear of train A.

Draw diagrams of these three events.

Knowing the rest length of train A and the relative velocity of the trains, what is the time interval between events 1 and 2 (as reckoned by the observers on train A)?
What is the length of train B as reckoned by the observers on train A, knowing the rest length of train B and the relative velocity of the trains?
Knowing the length of train B as reckoned by the observers on train A and the relative velocity of the trains, what is the time interval between events 2 and 3 (as reckoned by the observers on train A)?
As reckoned by the observers on train A, what is the time interval between events 1 and 3?
Now, do the same analysis for the observers on train B. As reckoned by the observers on train B, what is the time interval between events 1 and 3?