Solve Sliding Blocks with Weight 3w & Coefficient of Friction

[RoKe]

Here is the question:
Block A, with weight 3w, slides down an inclined plane S of slope angle 36.9 degrees at a constant speed while plank B, with weight w, rests on top of A and is attached by a cord to the wall. If the coefficient of kinetic friction is the same between A and B and between S and A, determine its value.
Ok, here's what I did:
x is the direction parallel to the slope and y is perpendicular. Forces in the x direction include the component of the weight of Block A (down the slope), the force of friction of S on A and the force of friction of B on A (both resisting the motion down the slope).
I did not include the plank B's weight as part of the force pushing the block down because the component of B's weight parallel to the slope is being countered by the tension in the string (I hope that's right).
The force of friction of S on A is equal to (u_k)4wcos39.9, and the force of friction of B on A is (u_k)wcos39.9.
F_net = 3wsin36.9 - (u_k)4wcos39.9 - (u_k)wcos39.9 = 0 (const. velocity)
The answer in the book is 0.450. I know I'm doing something wrong, but I want to move on to other questions so if someone can help out I'd appreciate it.

 

[Doc Al]

Except for a typo in your angles (it's 36.9, not 39.9), your analysis is correct and should give you the book's answer.

 

[RoKe]

So it does. I guess I was tired and was making mistakes in my calculations. Thanks! :)