Question

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?

Answer 1

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