I did my PPL fullt-time in UK. It was the hot summer of 2003 and I only lost one day for bad weather. It took 7 weeks. However, there are a few caveats to that. Firstly, I ain't no spring chicken and it's harder to learn a new skill the older you are. Secondly, it was a helicopter which is harder and has a higher average number of hours to get the licence.
Factors included unserviceability of the aircraft, my own workload with exams (I did three in advance) and my concentration levels.
Three weeks is pushing it I feel so budget for more. That would be 3 hours a day (allowing weekends to study) and that will be tough for a learner.
Cheers
Whirls