In the areas that are situated on extreme latitudes, you mentioned that there are four methods of calculating the times for the Eisha and Fajr prayers. How would these times be used for fasting in Ramadan? It seems that any of the methodologies enumerated could result in 20+ hour fasts, which does not seem reasonable for an entire month of fasting. It may become very difficult for one to fast for 20 hours and more.
