Calculating Tension and Motion in a Three-Box and Pulley System

[mbrmbrg]

Three boxes (A, B, and C) are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. Box A is on a frictionless table, boxes B and C hang over the side of the table.
The masses are mA = 30.0 kg, mB = 40.0 kg, mC = 18.0 kg.

(a) When the assembly is released from rest, what is the tension in the cord that connects boxes B and C?
60.1 N
(b) How far does box A move in the first 0.250 s (assuming it does not reach the pulley)?
0.202 m

Answers given are the book's answer's. (Actually, part b used to be my answer also, but I can't duplicate it...)

I'd like to start by calculating tension in the string connecting A to B&C, and then say that for A in the x direction, $$\Sigma\ F=T=m_Aa$$, and then use a to find delta x. Unfortunately, since the system is in motion, $$T\neq\ (m_B+m_C)g$$, and I don't know how to find it.

 

[Hootenanny]

Kinda like this question I think;
https://www.physicsforums.com/showthread.php?t=139444

 

[Ja4Coltrane]

All the blocks accelerate at the same magnitude, so first find that acceleration.

You know that net force on block C = McA (by Newton's second law) and you also know that net force on C=(Mc)(g)-T.

 

[mbrmbrg]

Kinda like this question I think;
https://www.physicsforums.com/showthread.php?t=139444

Exactly like this question, in fact, just different mass for C. Thanks! And wow, that dude can draw a neat diagram.