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Fundamental Misunderstanding of SR…?

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1. 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?

2. Homework Equations
##L=\frac {L_0} {\gamma}## , ##\Delta t = \Delta t_0 \gamma##

3. 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 whats wrong with my thought process and fix THAT rather than try to adapt to another method of solving.

EDIT: Figured out my mistake :)
 
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Simon Bridge

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