Question

A woman drives an SUV that gets ​13 mi/gal (mpg). Her husband drives a hybrid that gets 65 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 2 mpg and keep the hybrid as it is.


Option​ 2: They can buy a new hybrid that gets 80 mpg and keep the SUV as it is.

Which option will give them a better combined​ mpg?

Answer 1

Option 1 will give a better overall mileage.

Explanation:

The husband and wife travel the same number of miles each week.

Let's say each one travels x miles in 1 week.

Let e = fuel economy in mpg

Let v = amount of fuel in gallons

Let d = distance in miles

e = d/v

ve = d

v = d/e

Before modifying cars:

Wife:

d = x

e = 13

v = d/e = x/13

Husband:

d = x

e = 65

v = d/e = x/65

Combined fuel they both use in 1 week:

x/13 + x/65 = 5x/65 + x/65 = 6x/65 = 0.0923x

Option 1:

Wife changes to:

d = x

e = 15

v = d/e = x/15

Husband remains the same.

Combined fuel they both use in 1 week:

x/15 + x/65 = 13x/195 + 3x/195 = 16x/195 = 0.08205x

Option 2:

Husband changes to:

d = x

e = 80

v = d/e = x/80

Wife remains the same.

Combined fuel they both use in 1 week:

x/13 + x/80 = 80x/1040 + 13x/1040 = 93x/1040 = 0.08942x

The total fuel used in 1 week by both in terms of the miles, x, driven by both are:

Original case: 0.0923x

Option 1: 0.08205x

Option 2: 0.08942x

The lowest amount of fuel is 0.08205x in option 1.

Answer: Option 1 will give a better overall mileage.