Auto Insurance Claims: How many days can be demanded for loss of use car?

Question
QUESTION: A car was hit from rear. It cannot be driven. The driver reported the at fault car insurance two weeks after the car accident. Then the appraiser took another two weeks to complete appraisal and wrote two days to repair. The car owner is thinking to sell the car or get it repaired. But, in any circumstances the car owner needs to demand for the loss of use car. Can you tell how many days the car owner can demand for loss of use car, four weeks plus two days, two weeks plus two days, only two days or zero days if the car is eventually sold and why? Can you explain it?

ANSWER: You would need to show some economic loss, in the form of a car rental bill, bus fare, taxi fare, or similar.  Also, why was there a 2 week delay in reporting the claim?  Who caused the delay?  

---------- FOLLOW-UP ----------

QUESTION: The fact is the car owner has no car to use. So he has to ask someone to drive him by paying someone. The report delay (actually there is no requirements for how soon should the accident be reported) is the car owner reported his insurance but his insurance rejected his claim because he has only liability coverage. Then the car owner files the claim with the at fault car insurance. Can you directly answer the question now?

Answer
The person making the claim has a duty to mitigate his/her damages, and by waiting 2 weeks to report the claim, that was not done.  So I do not see why the insurer would owe for those 2 weeks, unless the insurer made some error during that time period.  The 2 weeks for the appraiser to inspect the vehicle should be covered, as well as the repair time.  You would need to document the economic loss in some manner.