How far was it from my Great Aunt's to my home?

Question

After visiting my Great Aunt Annie, I travelled home in her old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.

This meant that I could only travel along at a steady 30 km per hour and managed a paltry 20 km per litre of fuel.

At the start of the journey I had placed exactly 10 litres of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a litre per hour.

Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.

How far was it from my Great Aunt's to my home?

Answer 1

150 miles.

I was travelling at 30mph at a rate of 20mpg, so I was using 1.5 gallons every hour for the driving itself.

I was also losing 0.5 gallon every hour. In total, I was using 2 gallons every hour.

Therefore to use all of the 10 gallons I started with, I travelled for 5 hours.

5 hours at 30mph is 150 miles.