The oil paradox

We all know that the oil consumption by a car is almost proportional to its change in kinetic energy i.e. the more the velocity of a car, more is its oil consumption. Now consider this case. Car A Car B

Two cars (Car $A$ & Car $B$ ) are both moving with the same velocity in a straight road and both started at the same time. After some time Car $A$ accelerates to a velocity double of the initial velocity.

Now according to ground observer the change in velocity of the Car $A$ is = $1/2m(2v)^2$ - $1/2m(v)^2$ = $3/2mv^2$ and according to a observer sitting in car $B$ change in K.E. is $1/2mv^2$ (as relative velocity between two cars is $v$ ) So with different changes of kinetic energy in two frames does it mean that oil consumption for two frames are different. Can you provide a possible explanation for your answer?