my question about (Solving a value mixture problem using a system of linear equations)

Question

A family has two cars. During one particular week, the first car consumed 40

 gallons of gas and the second consumed 15

 gallons of gas. The two cars drove a combined total of 1825

 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

d= distance = 1825 miles

r= mpg = miles per gallon d/r = g = gallons

d= rg = 1825

a+b = 55 mpg

a = 55-b

A=40 gallons, B = 15 gallons

40a + 15b = 1825

40(55-b) +15b = 1825

2200 -40b +15b = 1825

25b = 375

b = 15 mpg for car B

a =55-15 = 40 mpg for car A

40(40) + 15(15) = 1600+225 = 1825