- The distance a particular car can travel in a journey starting with a full tank of fuel was investigated.
- From a full tank of fuel, 40 litres remained in the car's fuel tank after the car had travelled 80 km
- From a full tank of fuel, 25 litres remained in the car's fuel tank after the car had travelled 200 km
Using a linear model, with \(V\) litres being the volume of fuel remaining in the car's fuel tank and \(d \mathrm {~km}\) being the distance the car had travelled,
- find an equation linking \(V\) with \(d\).
Given that, on a particular journey
- the fuel tank of the car was initially full
- the car continued until it ran out of fuel
find, according to the model, - the initial volume of fuel that was in the fuel tank of the car,
- the distance that the car travelled on this journey.
In fact the car travelled 320 km on this journey. - Evaluate the model in light of this information.