The noon prayer would start and one would go to al-Baqi' and after having relieved himself he would perform ablution and then come, while the Messenger of Allah ﷺ would be in the first rak'ah, because he would prolong it so much. (Using translation from Muslim 454a)
لَقَدْ كَانَتْ «صَلَاةُ الظُّهْرِ تُقَامُ فَيَذْهَبُ الذَّاهِبُ إِلَى الْبَقِيعِ فَيَقْضِي حَاجَتَهُ ثُمَّ يَتَوَضَّأُ ثُمَّ يَجِيءُ وَرَسُولُ اللهِ ﷺ فِي الرَّكْعَةِ الْأُولَى يَطُولُهَا»