He had intercourse with his wife during the day in Ramadan and it is difficult for him to fast as expiation for that
Question

 
I have a question that is composed of two parts. The first part is: I had intercourse with my wife during the day last Ramadan. We have repented to Allah and we regret what we did. We want to offer expiation for this day, and I know that the fataawa of the scholars say that one must free a slave, and if that is not possible one must fast for two consecutive months, and if one cannot do that, then one must feed 60 poor persons, and my wife must do likewise if she did it willingly. But I find that it is too difficult for me and my wife to fast for two consecutive months, so will feeding 60 poor persons on my behalf and 60 on behalf of my wife as expiation for that day be permissible? 
The second half of the question is: Can I give food to fasting people who are travelling in cars and trains before the adhaan, or must the food actually reach poor and needy people? Because I do not know how to find 120 poor people in order to feed them.
Praise be to Allah.The one who has intercourse with his wife during the day in Ramadan has to free a believing slave. If that is not possible then he must fast for two consecutive months. If he is unable to do that, then he must feed sixty poor persons. The expiation is required in this order and it is not permissible to move from one to the next unless one is unable to do the first thing. This order was stated by the majority of scholars. So it is not permissible for you to turn away from fasting to feeding the poor if you are able to fast. If you are able to fast then you must do that. 
If you are unable to fast, then you must both feed sixty poor persons. It is essential that the people to whom you give food be in need. 
Based on that, it is not permissible to give food to people who are travelling in the manner you describe, because you do not know whether they are poor or not. 
But if you give food to one who appears outwardly to be poor, there is nothing wrong with that, but if you give it to anyone who is travelling, that is not permissible. 
If you cannot find any poor people, then you can delegate one of the trustworthy charitable organizations or the imam of a mosque to do that on your behalf, or you can ask your friends to help you find poor people. 
We ask Allah to accept your repentance. 
And Allah knows best.