Question

A woman drives an SUV that gets ​mi/gal (mpg). Her husband drives a hybrid that gets 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 its mileage by mpg and keep the hybrid as it is.
Option​ 2: They can buy a new hybrid that gets mpg and keep the SUV as it is.
Which option will give them a better combined​ mpg?

Answer 1

Hey, there are no numbers added to this problem but if you were to add them as I did down below that is how you solve this question!

Explanation:

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