We know the simple formula for calculating the mileage of our vehicle: it is given by the ratio of the distance traveled to the amount of fuel burnt. But this simple formula is not applicable until we have the (proper) techniques for the measurement of distance traveled and amount of fuel burnt. We explain it in what follows.
For the measurement of the distance we have the odometer installed in the vehicle. But for the measurement of the amount of fuel burnt, there is no meter with a properly graduated scale. There is a so-called fuel-meter which gives only an idea of how much fuel is left in the tank. We can not correctly measure the amount of fuel burnt, with the help of this meter.
Of course at a fuel station we can get a measured quantity of fuel. But even if we do so, we still do not know how much fuel was already there in the tank. Thus we do not know the amount of fuel present in the tank after getting fuel from the fuel station. However, there is a way to overcome this problem. We can get the tank completely filled. As we know the capacity of the tank, we now know the amount of fuel at distance between cities our disposal. Thus what we need to do is to note the odometer reading when we get the fuel tank completely filled; run the vehicle till the fuel is completely burnt out and note the odometer reading again. Thus subtracting the initial odometer reading from the final one we get the distance traveled and dividing it by the amount of fuel burnt, we get the mileage.
But there is a flaw in this method. If we completely burn the fuel of our vehicle, how can we reach the fuel station for the refilling? It is highly unlikely that the fuel will get completely burnt out just when we manage to reach the fuel station. Should we carry a can containing the fuel with us in our vehicle? We can, of course, if we were to calculate the mileage only once. But in reality, we need to calculate the mileage frequently in order to remain aware of the condition of the vehicle, which is essential for making decision when to get the vehicle serviced.