Just because you went out to play doesn't mean that the problem will go away.
Just because you went out to play doesn't mean that the problem has gone away.
ご質問ありがとうございます。
「遊びに行ったからといって問題が解決する訳ではない」は英語で「Just because you went out to play doesn't mean that the problem will go away.」と言えます。
上記の英文にてgo awayを覚えたいなら、「doesn't mean that the problem will go away」という使い方ができます。
しかし、文章の流れで下記の英文の方が自然だと思います。
Just because you went out to play doesn't mean that the problem has gone away.
上記の英文で「go away」の過去分詞を使用しました。
ご参考になれば幸いです。