Question

A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of l400 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?​

Answer 1

Car 1: 40 mpg; Car 2: 15 mpg

Explanation:

Car 1:

fuel: 20 gal

distance: x

efficiency: a

Car 2:

fuel: 40 gal

distance: y

efficiency: b

x + y = 1400

a + b = 55

efficiency equation:

efficiency in mpg = distance (in miles) / fuel used (in gallons)

Car 1:

a = x/20

Car 2:

b = y/40

We have 4 equations in 4 variables:

a = x/20

b = y/40

x + y = 1400

a + b = 55

20a = x

40b = y

20a + 40b = 1400

a + b = 55

20a + 40b = 1400

20b + 20b = 1100

20b = 300

b = 15

a + b = 55

a + 15 = 55

a = 40

Answer: Car 1: 40 mpg; Car 2: 15 mpg