If a fasting person travels during the day, he is allowed to break his fast

Yes, it is permissible
for a fasting person to break his fast if he travels during the day. This is
the view of Imam Ahmad (may Allaah have mercy on him). 

See al-Mughni, 4/345. 

This is indicated by the Qur’aan and Sunnah.  

Allaah says (interpretation of the meaning): 

“and whoever is ill or on a journey, the same number [of
days which one did not observe Sawm (fasts) must be made up] from other
days”

[al-Baqarah 2:185] 

Whoever sets out during
the day is “on a journey” so he may break his fast and avail himself of the
concession granted to travelers. 

With regard to the Sunnah: Ahmad (26690) and Abu Dawood
(2412) narrated that ‘Ubayd ibn Jabr said: I traveled with Abu Basrah
al-Ghifaari, the companion of the Messenger of Allaah (peace and
blessings of Allaah be upon him), in a ship from al-Fustaat in Ramadaan. He
set off then lunch was brought (according to a report narrated by Ahmad:
when we sent off from Marsana he ordered that his food be brought). Then he
said: ‘Come and eat.’ I said, ‘Can’t we still see the houses?’ Abu Basrah
said: ‘Don’t you want to follow the Sunnah of the Messenger of Allaah
(peace and blessings of Allaah be upon him)?!’ 

Ibn al-Qayyim said in Tahdheeb al-Sunan: 

This is evidence for
those who say that it is permissible for the traveler to break his fast on
the day on which he travels during the day. This is one of the two reports
narrated from Imam Ahmad, and the view of ‘Amr ibn Shurahbeel, al-Shu’bi and
Ishaaq. It was also narrated from Anas and it is the view of Dawood and Ibn
al-Mundhir.  

Shaykh al-Islam Ibn Taymiyah said in Majmoo’ al-Fataawa,
25/212. 

If a traveler sets out during the day, is it permissible for
him to break his fast? There are two well-known scholarly views, both of
which were narrated from Ahmad. The more likely to be correct says that that
is permissible, as it is proven in al-Sunan that some of the Sahaabah
used to break the fast if they set out during the day, and they said that
this was the Sunnah of the Prophet (peace and blessings of Allaah be
upon him). And it is proven in al-Saheeh that the Prophet (peace
and blessings of Allaah be upon him) intended to fast on a journey then he
called for water and broke his fast while the people were looking on. 

See al-Sharh al-Mumti’, 6/217. 

But he should not do that
until he has started his journey and left his city. It is not permissible
for him to break his fast while he is still in his city. 

Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’
(6/218): 

If he sets out during the day, he is allowed to break his
fast, but is that subject to the condition that he leaves his village first,
or if he has decided to travel can he break his fast (before departure)? 

The answer is that two views have been narrated from the salaf. The correct view is that he should not break his fast until he has left his city or village, because he is not yet traveling, rather he has the intention of traveling. Hence it is not permissible for him to shorten his prayers until he has left his town, so by the same token it is not permissible for him to break his fast until he has left his town.