A boy of five and his seven-year-old brother are recovering in hospital after surviving with their father for 10 days in a remote Australian national park before being discovered by a farmer.

The family found themselves with little food, no mobile phone reception and temperatures that rose to 38 Celsius (100 degrees Fahrenheit) after Steven Van Lonkhuyzen took a wrong turn during a road trip and his vehicle became bogged down in mud.

They were rescued after farmer Tom Wagner searched for them on his four-wheeled farm motorbike and found them after several hours in the Expedition National Park, north west of Brisbane.

"They were pretty hungry by the time I got to them and pretty happy to see me," Mr Wagner said.

Acting superintendent Mick Bianchi of Queensland Police said Mr Van Lonkhuyzen planned to drive from his home in Brisbane to Cairns using an inland route, but "quite simply, he took a wrong turn".

He said the boys were a little emaciated and dehydrated after their ordeal.

Mr Bianchi said the family had limited provisions but luckily it was stormy at times and they were able to collect rainwater in a plastic container.

Mr Van Lonkhuyzen tried to attract attention by laying out high-visibility items and lighting fires and Mr Bianchi said he made the right choice by staying with his vehicle.

"They were very trying conditions and it would have tested the family's relationship," he said.

He said Mr Van Lonkhuyzen attempted to establish routines with his children and keep them occupied.

The national park is not usually visited at this time of year because of the extreme weather conditions, Mr Bianchi said.

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Mr Wagner said the younger boy, Timothy, kept asking him if he had any eggs, while the older one, Ethan, appeared dehydrated. He said the father had given the limited food he had to his sons, who themselves had gone with little or nothing to eat for a week.

"Luckily it rained," he said. "Otherwise they would have perished."

Mr Bianchi said the boys' mother raised the alarm when the trio did not arrive at a friend's home in Cairns.