Answer:
Fuel efficiency of first car = 30 miles/gallon
Fuel efficiency of second car = 25 miles/gallon
Step-by-step explanation:
Given that:
Fuel consumed by first car = 40 gallons
Fuel consumed by second car = 15 gallons
Total distance drove by the two cars combined = 1575 miles
Sum of their fuel efficiencies = 55 miles/gallon
To find:
The fuel efficiencies of each of the cars = ?
Solution:
Fuel efficiency of a car is defined as the ratio of distance traveled in miles to the number of gallons used by the car.
Let the distance traveled by first car = [tex]x[/tex] miles
So, the distance traveled by other car = (1575 - [tex]x[/tex]) miles
Fuel efficiency of first car = [tex]\frac{x}{40}[/tex] miles/gallon
Fuel efficiency of second car = [tex]\frac{1575-x}{15}[/tex] miles/gallon
As per given question statement:
[tex]\frac{x}{40}+\frac{1575-x}{15}=55\\\Rightarrow 15x+1575\times 40-40x=55\times 40 \times 15\\\Rightarrow 25x=30000\\\Rightarrow x =1200\ miles[/tex]
Distance traveled by first car = 1200 miles
Fuel used by first car = 40 gallons
So, fuel efficiency of first car = [tex]\frac{1200}{40} = \bold{30\ miles/gallon}[/tex]
Distance traveled by second car = 1575 - 1200 = 375 miles
Fuel used by second car = 15 gallons
So, fuel efficiency of second car = [tex]\frac{375}{15} = \bold{25\ miles/gallon}[/tex]
