Praise be to Allah.
Jumu’ah prayer is waived for the traveller, so he should pray Zuhr, shortening it to two rak’ahs, and he may join it with ‘Asr at the time of the earlier or later prayer, according to what he needs to do. But it is better not to join it unless he needs to do so, if it will be difficult for him to perform each prayer at its own time.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The traveller does not have to pray Jumu’ah, and the evidence for that is the fact that during his journeys, the Prophet (blessings and peace of Allah be upon him) did not pray Jumu’ah, even though he had many people with him; rather he would pray Zuhr and shorten it. End quote.
Al-Sharh al-Mumti’ (5/10)
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked:
Is it better to join two prayers whilst travelling or to shorten prayers?
Offering each prayer at its proper time is better, if there is no need to join prayers. Usually when the Prophet (blessings and peace of Allah be upon him) was travelling, he would offer prayers at the proper times, and he only joined prayers on a few occasions. End quote.
Majma’ al-Fataawa, 24/19.
He also said (may Allah have mercy on him):
This shows that joining prayers is not part of the Sunnah of travelling, unlike shortening prayers. Rather it should only be done when there is a need for it, whether one is travelling or not. End quote.
Majma’ al-Fataawa, 24/64
Shaykh Ibn Baaz (may Allah have mercy on him) said:
The one for whom Allah has prescribed shortening of prayers, namely the traveller, is permitted to join prayers but the two concessions do not necessarily go together. He may shorten the prayers without joining them, and not joining them is better if the traveller has arrived at his destination and is no longer on the road, as the Prophet (blessings and peace of Allah be upon him) did in Mina during the Farewell Pilgrimage; he shortened the prayers but did not join them. But he both joined and shortened prayers during the campaign to Tabook, which indicates that this (concession) is prescribed to make things easy when there is a need for that. And he (blessings and peace of Allah be upon him) used to shorten and join prayers if he was on the road and was not staying in the place. End quote.
Majma’ Fataawa Ibn Baaz, 12/289
Usually when the traveller is on the road he needs to join the prayers, because that is easier for him, so that he will not have to make a further stop in order to pray, which may be difficult for him and delay his journey.
Based on that, it is permissible for you to pray Zuhr as two rak’ahs and join ‘Asr to it, at the time of the earlier or later prayer, according to what is easier for you.
And Allah knows best.