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Is it possible?
Student life, in partnership with UEA
I would say that it is pretty doable. I know that everybody works and writes at a different pace, but I still believe you will be fine if you make an effort. I can write 1000 words per day and I'm talking about science-based essays filled with a lot of recent research. If I can do it, you can do it! If you divide 7,500 words by 21 days, you get 360 words per day. Breaking it down this way, it becomes an easy job.
Writing 7,5k words will take a couple hours... you just need to plan and get on with developing the content to fill the words.