According to Official Guinness Records,
The greatest distance run by a relay team is 5,639.6 km (3,504.28 miles) and was achieved by Keep on Running (Ireland and UK) at St Colmans Sports Complex in Newry, County Down, UK, from 21 July to 8 August 2012.
Sean Goodman ran 422 laps of the 400m track which equates to 168,800 m (104.9 miles) during the course of the attempt. The runners ranged from 18-80 years old.
For a complete list of 2012 records, please visit 2012 Guinness Records in United Kingdom.