Fuel consumed by Car A = 20 gallons
Fuel consumed by Car B = 30 gallons
Total distance = 950 miles
Let, distance covered by Car A = X miles
As the total distance covered is 950 miles,
Distance covered by Car B = 950 - X miles
Efficiency is calculated as total distance travelled divided by total fuel consumed.
Efficiency of Car A = X/20 miles/gallon
Efficiency of Car B = (950 - X)/30 miles/gallon
It is given that sum of efficiencies is 40. So,
(X/20) + (950 - X)/30 = 40
X/20 can be represented as 3X/60 and (950 - X)/30 can be represented as (2*(950-X)/60) to make the denominator same.
(3X/60) + (2*(950-X)/60) = 40
Simplifying, we get
(3X + 1900 - 2X)/60 = 40
Simpifying further, we get
X + 1900 = 2400
X = 2400 - 1900
X = 500
So, distance covered by Car A = 500 miles
Distance covered by Car B = 950 - 500 = 450 miles
To calculate fuel efficiencies,
Efficiency of Car A = 500/20 = 25 miles/gallon
Efficiency of Car B = 450/30 = 15 miles/gallon
