Kinematics-Motion in one dimension

1. The problem statement, all variables and given/known data
Two points P and Q move in a straight line AB.The point P starts from A in the direction AB with velocity and acceleration [PLAIN]http://latex.artofproblemsolving.com/b/b/2/bb2c93730dbb48558bb3c4738c956c4e8f816437.png.At [Broken] the same instant of time Q starts from B in the direction of A, with a velocity http://latex.artofproblemsolving.com/0/5/5/0559ffc8c62a08ff533f3fcd1a5c1713a520755d.png and acceleration [PLAIN]http://latex.artofproblemsolving.com/3/7/a/37a9e7fca70e2dce829d902af2088735306bc1a3.png.If [Broken] they pass each other at the middle point of AB and arrive at the other end of AB with equal velocities, then prove that


2. Relevant equations
Let be the distance AB, be the time it takes to get midway.

Then, [PLAIN]http://latex.artofproblemsolving.com/b/2/c/b2c07b1586491a4fe17cfa89fa189a2ae96b7aa0.png. [Broken]

We also have [PLAIN]http://latex.artofproblemsolving.com/0/0/a/00a11d7cdd2ce508b54ea4592c254b2a6a2abc72.png.[/B] [Broken]


3. The attempt at a solution
I tried to do the problem by the above method but I am not getting the desired result despite many algebraic manipulations.Please can someone help me with this proof.

 

Sorry for using bold font.

 

Yes thank you , I got the solution.Here it is as follows:
From the first equation we get $$t_1=\frac{2u_1-2u}{f-f_1}$$
Now substituting the value of L in the second equation we get the desired result..