Some of the new cars monitor the fuel consumption and display the fuel efficiency for the driver in the form of a bar graph, as a function of time. Let us assume that in the first five minutes of a trip the fuel efficiency was 5 liters per 100km (lpk), in the second five minutes it was 10 lpk and in the third five minutes it was 20 lpk. What was the fuel efficiency during this 15 minute trip?
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The answer depends on how fast was the car is moving in each five minute segments, and that is unknown. Therefore we cannot answer the question.
To be more specific, let us assume that the car moves with velocity v 1 , v 2 and v 3 in the first, second and third five minutes, respectively. The total distance traveled is
d = ( v 1 + v 2 + v 3 ) t
where t = 5 m i n . The fuel burned during the first five minutes is M 1 = γ 1 v 1 t , where γ 1 = 5 l p k . There are similar expressions for the other time intervals. The total amount of fuel used during the trip is
M = M 1 + M 2 + M 3 = t ( v 1 γ 1 + v 2 γ 2 + v 3 γ 3 )
The overall efficiency is
γ = d M = v 1 + v 2 + v 3 v 1 γ 1 + v 2 γ 2 + v 3 γ 3
If, for example, the car moves with constant velocity, we get
γ = d M = 3 γ 1 + γ 2 + γ 3 = 1 1 . 6 6 l p k
However, all kinds of other answers are possible with different choices of velocities.