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»  

His father said: "The Messenger of Allah ﷺ used to lead us in prayer, and he would recite in the first two rak'ahs and make us hear some verses. And he would make the (first) Rak'ah lengthy in Zuhr, and also the first rak'ah." Meaning in Subh. (Using translation from Nasāʾī 974)  

عَنِ النَّبِيِّ ﷺ قَالَ كَانَ «يُصَلِّي بِنَا الظُّهْرَ فَيَقْرَأُ فِي الرَّكْعَتَيْنِ الْأُولَيَيْنِ يُسْمِعُنَا الْآيَةَ كَذَلِكَ وَكَانَ يُطِيلُ الرَّكْعَةَ فِي صَلَاةِ الظُّهْرِ وَالرَّكْعَةَ الْأُولَى يَعْنِي فِي صَلَاةَ الصُّبْحِ»