Answer:
Option 1 will give a better overall mileage.
Step-by-step 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.
