dear raj , here is the sol of ur question ...

let initial  position of A & B are P , Q ....

after time t when they meet then let this point be O ...

now joint PQO , this will be a right angled triangle with PO as hypotenuse ...

accleration of A & B are alfa & beta ....

displacement of B  = (beta)t²/2  = QO           ...............1               ( by using s = ut + at²/2 )

displacement of A after time t = (alfa)t²/2 = PO             ..............2   

PQ = L               (given)

now using pythogorus theorem

PO² = PQ² + QO²

substituting these values from eq 1, 2  ,3

 ((alfa)t²/2)² = ((beta)t²/2)² + L² 

 t = {4L²/[(alfa)² - (beta)²]}

approve if u like my ans

let initial  position of A & B are P , Q ....


after time t when they meet then let this point be O ...

now joint PQO , this will be a right angled triangle with PO as hypotenuse ...

velocities of A,B are u & v ....

after time t ,

 displacement of A = ut  =  PO                             (speed = distance/time)

 displacement of B = vt  =  QO

 PQ = L

now  applying pythogorus theorem

PQ² + QO² = PO²

 t =[L²/u²-v²]^1/2

this is the required time

Specify page numbers and question numbers , i can't see the full question !