Question

A woman drives an SUV that gets 11 mi/gal (mpg). Her husband drives a hybrid that gets 60 mpg. Every week, they travel the same number of miles. They want to improve their combined mpg. They have two options on how they can improve it.
Option 1: They can tune the SUV and increase it mileage by 1 mpg and keep the hybrid as it is.

Option 2: They can buy a new hybrid that gets 75 mpg and keep the SUV as it is.

Compute the combines mpg for each option.

Option 1 Answer? : Option 2 Answer? :

(round to one decimal place as needed.

Answer 1

Suppose s and h are the mileage numbers for the SUV and Hybrid, respectively. Then if each vehicle drives 1 mile, the total gas consumption is
.. 1/s +1/h
Then the combined mileage is
.. 2/(1/s +1/h) = 2sh/(s+h)

Option 1: s=12, h=60
.. mpg = 2*12*60/(12+60) = 20

Option 2: s=11, h=75
.. mpg = 2*11*75/(11 +75) = 1650/86 ≈ 19.2

In summary,
.. Option 1: 20.0 mpg
.. Option 2: 19.2 mpg

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It usually works out best to increase the efficiency of the least-efficient contributor, as here.