Spacetime diagram based question.

[ronsonol]

Homework Statement

A Spaceship is moving with speed ß=4/5.

Its length at rest is 1sec. A light is turned on at the rear of the ship, reflected back from a mirror at the front.
a.) How long does an observer at rest say it takes for the light to return to the rear of the ship (total round trip time)?
b.) How long did the light take to go from the rear to the front?
c.) How long did the light take to go from the front to rear?
d.) Use the results above to determine how far out of synchronization an observer at rest says the ship's front and rear clocks are.

∆T = 2s (proper time = 2seconds) light shining from rear to front back to rear.
y=5/3

Homework Equations

∆t=y (∆t' +ß∆x')
∆T - ∆t≈=-0.5v^2∆t

The Attempt at a Solution

For Part A I used the 1st equation:
∆t = (5/3)(2s + (4/5)(0)) = 10/3s
I'm not sure if I set it up correctly, but I got it right.

I am still trying to figure out part B and part C and have attached a diagram.

Part D I'm not sure exactly how I got the correct answer but I used the 2nd equation to estimate the difference:
2-(10/3) = -4/3s

 

[ronsonol]

Since this thread was moved from the Advanced to Introductory section, I thought it would be appropriate to bump, hopefully someone can offer a hint for me to continue. Thanks in advance.