This phrase implies that you are focused on a goal of yours to travel and work. If however, you used "I would like to" instead of " I want" this would suggest that you wouldn't mind and wouldn't be as serious.
このフレーズは、旅行をしながら働くという目標に向かって集中しているというニュアンスです。
もし "I want to" の代わりに "I would like to" を使うと、そこまで真剣でないニュアンスになります。
Here you want to be able to explain that you want to be able to both travel and work at the same time.
You can be specific by stating that you want to travel the world while traveling. For example: 'I'd love to work while traveling the world'.
In some cases you don't need to be specific as the other person will most likely interpret this as wanting to travel the world anyway.
So you can say the following:
I'd love to travel and work and the same time
I want to work remotely while traveling
これは、仕事をしながら世界を旅行したいことを伝えたいということですね。
仕事をしながら世界を旅行したいと具体的に伝えてもいいです。
例えば：
'I'd love to work while traveling the world'.
（世界を旅しながら仕事をしたいです）
世界を旅したいという意味だと相手に伝わるであろうときには、具体的に言う必要がないこともあります。ですから、次のように言えます。
I'd love to travel and work at the same time（旅行しながら仕事をしたいです）
I want to work remotely while traveling（旅をしながら遠隔勤務をしたいです）
I'm seeking a profession that involves traveling around the world.
I'm looking for a job that requires traveling the world.
I want to have a career that affords me the time to travel around the world.
Seeking means looking for or pursuing. A profession that involves traveling would be a job or career that includes the requirement to travel as part of the job.
"Requires traveling the world" is a way to impress that traveling the world is a mandatory part of the job. This would mean that traveling is a big part of the job.
The expression "affords the time," in this case, means to allow the time. If time is afforded to someone while he/she is employed, this typically means that the job pays well and includes the option to take extended time off for traveling.
"Seeking" は「探し求めている」という意味です。"A profession that involves traveling" は、仕事の一部に旅行をすることが含まれる仕事をいいます。
"Requires traveling the world" は、世界を旅することが求められる仕事を表します。旅をすることが仕事の重要な部分を成しているという意味合いです。
"Affords the time" はこの場合「時間の余裕がある」という意味です。これは一般的に、もうけが良くて旅行のために長期の休暇が取れる仕事を表します。
I would like to be able to work while traveling the world.
This sentence could mean that you would like to work remotely to be able to travel whenever you like. It could also mean that you would like a job that allows you travel around the world such as a flight attendant or cruise ship member. I hope that this helps. :)
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