How Does Time Dilation Affect Signal Reception from a Fast-Moving Spaceship?

[Huy]

Homework Statement

We observe a spaceship moving away from the Earth at a velocity of v = 0.866c. The spaceship emits two light signals, the second one 4 seconds (Delta T') after the first one (measured on board). What is the time interval (Delta T) between the arrival of the two light signals on earth?

Homework Equations

Time dilation, Lorentz contraction, Lorentz transformation, invariance of space-time

The Attempt at a Solution

I basically applied Lorentz transformation: www.i.imgur.com/ylfOJ.jpg (please copy & paste, I can't include a link in my first ten posts...)
However, using my approach I arrive at Delta T = 14s, whereas the solution says it should be 15s. I hope my writing is readable and I'm sorry I didn't know whether this belongs to intro- or advanced physics, the educational system in my country differs from the U.S.' a lot...

Thanks for any help in advance.

 

[jedishrfu]

did you factor in that the spaceship has moved further away in four seconds? This would delay the second signal a bit more.

 

[Huy]

I'm pretty sure I did, because basically, what I am doing in my solution is applying the Lorentz transformation to the inertial system of the spaceship which is moving away with constant velocity.