A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 30 gallons of gas. The two cars drove a combined total of 950 miles, and the sum of their fuel efficiencies was 40 miles per gallon. What were the fuel efficiencies of each of the cars that week?

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