How do I agree a price for borrowing my dad's car when he keeps saying it's free?

Dad offered his spare car for the six weeks I'd be training in the next town. "Just put the petrol back," he said. Then he asked me to record the mileage for every journey.

I haven't started borrowing it. We still need to confirm the driving permissions and insurance arrangements before I do. On the money side, I offered $20 a week towards wear, and he waved that away. He says the mileage notes would help him keep track of the car, not calculate a bill.

I believe him, but I also know I'd worry about whether taking it to a friend's house looked like abusing a favour. Public transport would cost about $160 a month under the fares I've checked and take longer. Borrowing could be convenient, yet 'free' feels less simple when I don't know what use he expects.

Would you settle the permitted trips and petrol arrangement without forcing him to take payment, insist on a contribution, or use public transport? I want to accept help without privately turning every mile into a debt I think he hasn't named.