Question: If a man enters the mosque after the call to prayer (Adhan) has been made, meaning the time for prayer has started, and he is in a hurry to travel or attend to some other task, can he pray alone before the congregation starts and leave the mosque?
Answer: When a person goes to the mosque and the Adhan has been called, he should not leave the mosque until he has prayed, as it is prohibited to leave the mosque after the Adhan. Ibrahim bin Muhajir narrated from Abu Sha’tha, who said:
"We were sitting in the mosque with Abu Hurairah (may Allah be pleased with him) when the Mu'adhdhin called the Adhan. A man got up and walked out of the mosque. Abu Hurairah kept looking at him until he left the mosque. Then Abu Hurairah said: 'As for this man, he has disobeyed Abu al-Qasim (peace and blessings be upon him).'" (Sahih Muslim: 655)
If a person needs to travel and does not have time, he should not come to the mosque. He should proceed with his journey. If he comes to the mosque, he should pray with the congregation and then leave. He should not pray alone and leave the mosque.
A person knows their own needs and how long it takes to pray in the mosque. Therefore, if someone needs to leave urgently, they should attend to their need. If they can pray with the congregation, then they should go to the mosque.
In an emergency situation, if someone has to leave the mosque after the Adhan, they may do so, but they should not pray alone in the mosque before the congregation.
Sheikh Maqbool Ahmed Salafi (may Allah preserve him) / Jeddah 
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