Stephanie Lylak heard Joe Hockey’s suggestion that poor people do not own cars, or at least do not drive them very far, before she ferried her two eldest children to primary school in the family's 16-year-old Commodore.

The single mother from Frankston followed the reaction as she dropped her toddler off with her mother, who provides the childcare she cannot afford.

As the Treasurer later defended his claim that increasing the petrol tax would not be felt as hard by the poor, she was driving to Monash University's peninsula campus, where she is studying nursing in the hope of eventually earning more than the $24,000 a year she receives in welfare and family payments.

While Ms Lylak limits her driving to cut costs, she said she spent about $100 a week on petrol – about 20 per cent of her payments – as she travelled between home, school, children’s sporting commitments, university and shops.

Ms Lylak said the proposal to increase the fuel excise was "a joke”, as she already struggled to make ends meet and was forced to accept charity from welfare groups.

“The money we receive barely feeds us, so I don't know how we’re expected to get around,” she said. “Some days it’s already the difference between feeding the kids or yourself.

"The kids come first so you have to go without sometimes. I can’t afford for my pay to go down any more than what it is already."

She bought the car last year for $3000 with advance payments from Centrelink and a string of loans from a no-interest lender, family and friends. But because she could not afford to take it to a mechanic, she had resorted to servicing it herself. “It’s just changing the oil, spark plugs, very, very basic," she said.

Emma King, chief executive of the Victorian Council of Social Service, said poorer people living in growth corridors, regional and rural areas were more reliant on cars and incurred much higher travel costs than people living near the city.

She said the cost of running cars in some transport-poor areas was as much as half a family's household expenditure.

“We’ve got poor people who are heavily reliant on cars, who are travelling longer distances, and for many of them they have higher running costs," she said. "Any impact on the cost of petrol impacts people who are poorer the hardest."

Whittlesea Community Connections team leader Peta Fualau said the pain was felt by low-income families in growth corridors, who often had to run two cars because of a lack of public transport.

“Aside from living further away from infrastructure and transport, they’re running cars that are older and that are often petrol-guzzlers, because there’s no infrastructure that allows them to catch public transport,” she said.