The family of an 84-year-old woman who went missing in a national park in Western Australia last week say they feel like they have won the lottery after she was found weak but alive on Sunday.

Patricia Byrne shocked police and rescue workers after she appeared from bushland in the the Stirling Range national park, in the state’s south-west. She had not been seen since Thursday, and her disappearance sparked a land and air search effort of Mount Trio.

Byrne has been “weakened” but was able to speak to her rescuers, police say. Her medical condition was still being assessed at the Albany health campus.

The 84-year-old had no food or water with her during her 72-hour ordeal, and had endured 37C temperatures on Friday.

Her son, John Byrne, said his mother had drunk from puddles of water to stay alive. “I really struggle to see how she could survive that day,” he said.

“Intense heat, stifling heat – Mum’s 84 years old, just wearing a shirt and a pair of shorts.”

Her grandson Blair Coatsworth said the rescue was “awesome news” after fearing she was dead. “The police officer walked over to us and we thought we were getting the worst of the worst and then he just hit us with the best lotto win,” he told reporters.

“We always knew she was a tough old goat. She’s probably the hardest 84-year-old you’d know. She would take on a gang of people, that woman, and to hear she came out the way she did was sort of what you’d expect from her.”

Sergeant Allan Mallard found Byrne walking along the side of the road, about 4km from where she was last spotted. He said that at first he hadn’t recognised her.

“I said, ‘What’s this person doing on the side of the road, she shouldn’t be here,’” he said.

“It was a bit of a shock, to be fair,” he told the Nine Network. “I was like, ‘Stop, stop the car,’ and tried to jump out of the car while it was still moving.”

More than 40 State Emergency Service volunteers, WA police, park ranges and the tracker dog team had combed the area since Thursday.