Performing five daily prayers on time is an essential duty in Islam and every individual Muslim who reached puberty is supposed to pray five times in a day. In the Qur’an and Sunnah there are many religious texts that emphasize on performing five daily prayers on time with utmost care. Islam is a religion which consider every aspect of human nature when offering religious commands or prohibiting from certain acts, food, behaviors etc. Similarly, five daily prayers is a command which human nature can carry out it without meeting extreme difficulty. Nevertheless, there is a burden in every religious duty thus we are called as “mukallaf” which means a person who is loaded with burden and responsibility. But, these burdens are not beyond human capacity. However, whenever performing a religious duty brings extreme hardship and difficulty upon Muslims Islam has given some easiness (rukhsah). For example, it is permissible to shorten prayers when a person is a traveler or break fasting during Ramadan. Similarly, combining prayers (noon prayer (Zuhr) with afternoon prayer (Asr) or evening prayer (Maghrib) with late evening prayer (Isha) is permitted due to some difficulties and hard conditions. Contemporary Muslims have faced many problems which were not seen before. One of them is school constrains which prevent students perform five daily prayers on time with diligent care. Thus, some contemporary scholars gave fatwa (religious verdict) to combine prayers and perform two prayers at once. Therefore, I would suggest this student to combine noon prayer with afternoon prayer at home if the conditions is hard. Nevertheless, heart and conscience is the best fatwa giver, thus ask your heart…
However, in this case if you are sure you will not have time to perform each prayer on time you can act according to one of other four madhabs. Shafii madhab has the ruling for merging dhuhr and asr and also for maghrib and isha. Therefore, you can follow the ruling if Shafii school for this specific issue due to hardship.
Merging at home is not the same with doing at the actual time. I think zuhr can be done at lunch time and Asr right after the school ends at an empty room. If no room or place is found, maybe in the bus or in the car while sitting. Then they might be re-done at home. Allah knows the best.