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Shoe: Kitty, how many hours a day did you work last week and when do you think you'll be exhausted? (1)
Shoe: Kitty, how many hours a day have you worked last week and when do you think you'll be exhausted? (2)
Kitty: Really, Shoe, I've already exhausted myself, especially physically, and that's exactly why I want to suspend my work.
In Shoe's questions past, present and future events are mixed.
Which is the correct time frame,
(1) "did you work", or (2) "have you worked"?
Usage of Present Tense and Future Tense with Simple Past or Present Perfect doesn't really matter; what matters is whether the confusing verb will be in Simple Past or in Present Perfect.
To determine which tense will be used follow these simple steps:
1) Has the Time Period finished? If yes- Simple Past, else- Present Perfect.
2) Is the information old? If yes- Simple Past, else- Present Perfect.
3) Is the action time specific? If yes- Simple Past (If it falls under definite past), else- Present Perfect.
4) Has the action finished? If yes- Simple Past, else- Present Perfect. (Most important)
This rule is mostly applied to see which tense is the most appropriate. If the result of the action still persists in the present, it is present perfect, otherwise it's Simple Past.
Example-
I have lived in California for five years. (Still living)
I lived in California for five years. (Don't live now)
In your cited example, from the context, it seems that the time period of Kitty's work hasn't finished yet and in the coming time, she is not going to work more for her fatigue and the ailment of the work has been added to her body making her exhausted when the speaker is speaking to her. So the actions (being fatigued) of her work still persists. So the most appropriate tense would be Present Perfect. Hence, your "Have you worked" would be the correct tense here.
Also note that, an additional "in the" before the week is required to make the time continuous as suggested by StoneyB. A mere "last week" means the week has gone past and the continuity of Kitty's work is not properly reflected. But if we add "in the" in front of week, it becomes continuous. So the proper way to put the sentence would be:
Shoe: Kitty, how many hours a day have you worked in the last week and when do you think you'll be exhausted?
To read more, visit Simple Past vs Present Perfect or ELC study Zone.
