Minimum Distance for Breaking Fast and Shortening Prayers
Question

What is the minimum distance of travelling at which fasting is excused?
Praise be to Allah.The majority of scholars are of the view that the distance at which a traveller may join prayers and not fast is forty-eight miles. 
Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni: 
The view of Abu `Abd-Allah [i.e., Imam Ahmad] is that it is not permissible to shorten the prayers for a distance of less than sixteen Farsakhs, and a Farsakh is three miles, so the distance is forty-eight miles . This was the estimation of Ibn `Abbas. He said: From `Usfan to Makkah, or from Al-Taif to Makkah, or from Jeddah to Makkah.” 
Based on this, the distance at which it is permissible to shorten prayers is the distance of two days’ travel aiming directly for that destination. This is the view of Ibn `Abbas and Ibn `Umar, and the view of Malik, Al-Layth and al-Shafi`i. 
The equivalent in kilometres is approximately 80 km. 
Shaykh Ibn Baz said in Majmu` Al-Fatawa (12/267), explaining what is meant by travelling: 
“The view of the majority of scholars is that this is equivalent to approximately eighty kilometres for one who travels by car, plane or ship. This distance is what is called travelling according to the custom of the Muslims. So if a person travels by camel, car, plane or ship, for this distance or more, he is regarded as a traveller.” 
The Standing Committee was asked (8/90) about the distance at which a traveller may shorten his prayers, and can a taxi-driver who covers more than three hundred kilometres shorten his prayer? 
They replied: 
“The distance at which a traveller may shorten his prayers is approximately 80 km according to the view of the majority of scholars. It is permissible for a taxi driver or anyone else to shorten his prayers, if he is going to cover the distance mentioned at the beginning of the question, or more.” 
Some scholars are of the view that travelling is not to be defined by a specific distance, rather it should be defined according to custom: whatever people customarily regard as travelling is the travelling to which the Shar`i rulings apply, such as joining and shortening prayers, and not fasting . 
Shaykh Al-Islam said in Al-Fatawa (24/106): 
“The evidence supports those who regard shortening prayers and not fasting as being applicable to all types of travel and do not single out one kind of travelling to the exclusion of another. This view is the correct one.” 
Shaykh Ibn `Uthaymin was asked in Fatawa Arkan Al-Islam (p. 381) about the distance at which a traveller may shorten his prayers and whether it is permissible to join prayers without shortening them. 
He replied: 
“The distance at which a traveller may shorten his prayers was defined by some of the scholars as being approximately eighty-three kilometres, and some defined it as being what is customarily regarded as travelling, even if the distance is not 80 km, and that what the people say is not travelling should not be regarded as such, even if it is as far as one hundred kilometres. 
The latter view is the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him), because Allah did not state a specific distance that makes shortening prayers permissible, and neither did the Prophet (peace and blessings of Allah be upon him). 
Anas ibn Malik (may Allah be pleased with him) said: If the Messenger of Allah (peace and blessings of Allah be upon him) set out for a journey of three miles or three farsakhs, he would pray two Rak`ahs. (Narrated by Muslim, 691) 
The view of Shaykh Al-Islam Ibn Taymiyah is closer to what is correct. 
There is nothing wrong, if there is a conflict between customary views, in going by the opinion which suggests that travel should be defined in terms of distance, because this was the view of some of the Imams and scholars and Mujtahids. So there is nothing wrong with that in sha Allah. But so long as custom gives a clear definition, then referring to what is customary is the right thing to do.”
And Allah knows best.