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We have two vehicles

A: old truck that does 17 mpg (13.84 l/100km)
B: old car that does 47 mpg (5.00 l/100km)

We are looking to replace one of these vehicles with a new one (of the same size)

C: new truck 19 mpg (12.38l/100km)
D: new car 61 mpg (3.85l/100km)

So which vehicle should we replace to save fuel? The old truck or the old car to end up with.

  1. AD (old truck + new car)
  2. BC (new truck + old car)

Read bellow once you have your anwser:

The way I solved this:

A: Old truck 13.84 l/100km + D: new car 3.85 l/100km = 17.69 l/100km,
B: New truck 12.38 l/100km + C: old car 5.00 l/100km = 17.39 l/100km

Combination BC uses less fuel.(0.31l less). Now using mpg:

17mpg + 61mpg = 78mpg
19mpg + 47mpg = 66mpg

Making the combination AD a better choice.

Why the exact opposite answer? What am I missing here?

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For your first trial you have that AD needs 0.31l more to drive 100km and, hence, BC is better. You make all the vehicles drive the same distance and, at the end, you sum up their fuel consumption (thus, you can sum their consumption rates).

But in your second trial, since you are using mpg, each vehicle is driving a different distance, so you cannot sum the rates same way you do in the first case.

If you assume that there is no distinction between the itineraries of the car and of the truck, then your first answer is the correct one. If you assume that you have to use the same amount of fuel in both vehicles (which seems to be a bit ankward), then your second answer is correct.

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