Eaton, who was appointed Premier’s chief operating officer and executive director earlier this month, was completing for the third time in the Original Mountain Marathon in the Howgills hills in Cumbria.
The endurance race involved 11 hours of racing over two days, with full packs and camping overnight in biting weather.
The Eatons were raising funds for the Masanga hospital in Sierra Leone.
Masanga hospital
To donate money to the charity visit http://uk.virginmoneygiving.com/team/Eaton10 , or send a cheque, made payable to Masanga UK, to Geoff Eaton at Building Ct3, Centrium, Griffiths Way, St Albans, Hertfordshire, AL1 2RE.
The jungle hospital of Masanga has 100 beds and serves children, mothers and men from a wide catchment area.
About 150,000 patients have been treated so far at a cost of just £5 per patient.
The hospital is currently staffed by medics from Denmark, Norway, Holland and the UK, working in an international partnership.