Bodies connected by a light inextensible string on an inclined plane

[Bill Gregoryson]

Homework Statement

Connected bodies by light inextensible string on an inclined plane

Relevant Equations

F = ma, v^2 = u^2 + 2as, s = ut + 1/2at^2

Here is the question (Qu 9):

Here is what I have attempted:
assumed that the accelerations are equal, found a value for the acceleration, thus worked out the time taken for A to reach the bottom.
then assumed that the tension becomes 0 once A hits the floor, and then worked out B's new acceleration and hence the time taken for B to hit A.

How am I allowed to assume that the acceleration is equal?
How do we know that B does not at any point move slightly faster such that the string becomes "squashed"?

I get the answer 1.29, which according to the answers is incorrect.

 

[kuruman]

How am I allowed to assume that the acceleration is equal?

You don't need to assume anything. Just find the acceleration of each block as if the other one were not there. Are the expressions equal or not?

How do we know that B does not at any point move slightly faster such that the string becomes "squashed"?

If the blocks start from rest and their accelerations are equal, can this happen?