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?

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lilygomez lilygomez · Answer 1 · 2021-02-25T03:38:57+01:00

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!

Step-by-step 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