Fundamental Misunderstanding of SR…?

[member 545369]

Homework Statement

A space explorer travels in a spaceship with v = 0.9c. She goes from Earth to a distant star that is 4 light years away (again, measured from Earth). What is the distance measured by the explorer and how long will she say it took her to get there?

Homework Equations

$L=\frac {L_0} {\gamma}$ , $\Delta t = \Delta t_0 \gamma$

The Attempt at a Solution

I solved the first part perfectly fine and got the answer of $L = 1.7$ light years. When solving for $\Delta t$ I realized that I didn't have $\Delta t_0$. No problem! I just solved the equation $\frac {L_0} v$ for $\Delta t_0$ and got a value of $\frac {40} {9}$ years. Since $\gamma \approx 2.3$ I just multiplied $2.3$ by $\frac {40} {9}$ and got a value of $10.2$ years. The actual value is 1.9 years, which happens to also be $\frac {\Delta t_0} {\gamma}$ but I don't see why I'm wrong!

NOTE: I know that there is another solution to this problem and perhaps it is a bit simpler. I would like to focus on what's wrong with my thought process and fix THAT rather than try to adapt to another method of solving.

EDIT: Figured out my mistake :)

 

[Simon Bridge]

EDIT: Figured out my mistake :)

Well done - what was it?