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  1. By this time next week, I will have worked on this project for twenty days.

  2. By this time next week, I will work on this project for twenty days.

Do they both mean the same? If not, what is the difference?

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Alternatively, if the project won't have been finished by this time next week, and you will continue to work on it, you say: By this time next week, I will have been working on this project for twenty days.

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The first sentence is grammatically correct, the second isn't. When you say 'by this time', you generally talk of an to an event that would have completed before the time you refer to.

I will work for 20 days on this project for 20 days refers to some work you are yet to do and doesn't go well with 'By the time next week'.

On the other hand, By this time next week, I will not have worked on this project for 20 days IS ALSO grammatically correct, since you are again technically referring to a completed event - that is not have worked

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