Samia set off on her bicycle to visit her friend, traveling at an average speed of $17 ~kilometers~ per~ hour$. When she had gone half the distance to her friend's house, a tire went flat, and she walked the rest of the way at $5 ~kilometers~ per ~hour$. In all it took her $44~ minutes$ to reach her friend's house. In kilometers rounded to the nearest tenth, how far did Samia walk? If the answer is $x$ kilometers, what is the value of $10x$?

Let's think step by step and output the final answer within \boxed{}.
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