Combining the prayers is permissible in the light of ahadeeth as we'll establish this in the light of authentic traditions in the lines below , inn sha Allah.
Ibn 'Abbas reported:
I observed with the Messenger of Allah (ﷺ) eight (rak'ahs) in combination, and seven rak'ahs in combination. I (one of the narrators) said: O Abd Sha'tha', I think that he (the Holy Prophet) had delayed the noon prayer and hastened the afternoon prayer, and he delayed the sunset prayer and hastened the 'Isha' prayer. He said: I also think so.
Sahih Muslim , Book 6, Hadith no. 65 (Grade=Sahih)
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Ibn Abbas said:
"Allah's Messenger combined the Zuhr and Asr (prayers), and the Maghrib and Isha (prayers) in Al-Madinah, without being in a state of fear, nor due to rain."
Tirmidhi, book 2, hadith 39 (Grade=Sahih)
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The above mentioned tradition has also been reported in tirmidhi by 'Uqail through a different chain of narrators. He said:
He would delay the evening prayer till he combined the evening and the night prayers when the twilight disappeared.
Famous scholar of hadith Al-bani has graded it as Sahih.
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It was narrated from Ibn 'Abbas that the Prophet (ﷺ) used to pray in Al-Madinah combining two prayer. Joining Zuhr and 'Asr, and Maghrib and 'Isha', when there was no fear nor rain. It was said to him:
"Why?" He said: "So that there would not be any hardship on his Ummah."
Sunan-An Nisai, Vol 1, Book 6 (Grade= Sahih)
Conclusion:
In the light of above traditions, (none of which is da'eef i.e. weak) we can establish that there is no harm or sin in combining zuhr and asr as well as maghrib and isha prayer whether one is travelling or staying at a place. Allah knows the best.
