## Tuesday, September 9, 2014

### Household Fuel Efficiency -- Ford Focus and Yukon GMC

Household Fuel Efficiency  -- Ford Focus and Yukon GMC

This post looks at the combination of driving for a Ford Focus and a GMC Yukon that will lead to household fuel efficiency of 21.

Question:   A household initially has only one vehicle the GMC Yukon.   A second vehicle – the Ford Focus is purchased.    The combined fuel efficiency of the GMC Yukon is   17 mpg.   The combined fuel efficiency for the Ford Focus is 31 mpg.

GMC Yukon fuel Efficeincy 2013

Ford Focus fuel efficiency 2014

What percent of household travel must occur in the Ford Focus for the household fuel efficiency to be equal to 21 mpg?

Answer:      Fuel efficiency is the ratio of miles driven to gasoline consumed.

FE=Miles/Gallon

Define F as miles driven in Focus and Y as miles driven in Yukon.

21=(Y+F)/(Y/17 + F/31)

Here the numerator Y+F is total miles driven and the denominator (Y/17 + F/31) is gas consumed so the ratio of the two is fuel efficiency in miles per gallon, which is set equal to 21.

Let’s assume without loss of generality that F+Y=10000.  This means Y=10000-F.

Plug this in we get:

21= 10000/((10000-F)/17) + F/31

Turn it upside down

(1/21) = ((10000-F)/17)  +(F/31))/10000

Multiply by 10000

10000/21   = (10000-F)/17    + (F/31)

Continue simplifying:

10000/21 -10000/17   = ( (1/31) –(1/17)) * F

or

F   = (10000/21)  - (10000/17)/ ((1/31) –(1/17))

F=4217.7

In other words for the two-car household to get 21 mpg 42.2% of the driving must occur in the Focus and the remaining 58.8% of driving must occur in the Yukon.

Confirm that:

21= 100000/((4217.7/31)+ (5782.3/17))