System Analysis - Simplifying with Transfer Functions

[ConnorM]

Homework Statement

Sorry for the pictures, I'd normally write out the problem but it is mostly diagrams.
Question and work attached. I am looking for help with part (a) right now, the transfer function I obtain is shown at the end of my work.

Homework Equations

Knowledge of Laplace transforms
Knowledge to simplify a block diagram

For Connor2.JPG the second diagram I drew there is an error. The 5 and 3 should switch spots like they were in the diagram above it.

 

[LvW]

What is your question?
You have solved the task (including part a) - and the result is correct.

 

[ConnorM]

I just wasn't sure if what I had done was correct. So I wanted to get someone else to look at it.
Thanks!