A family has two cars During one particular week the first c

A family has two cars. During one particular week, the first car consumed 25 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1225 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?

Solution

Let the fuel efficiencies of the first car and and the second car be x miles/gallon and y miles per gallon. During one particular week, the first car consumed 25 gallons of gas and the second consumed 40 gallons of gas so that the distances travelled by the first car and and the second car were 25x miles and 40y miles respectively. Hence 25x+40y = 1225, or, on diving both the sides by 5, we get 5x+8y = 245…(1). Further, the sum of the fuel efficiencies of the first car and and the second car was 40 miles per gallon so that x +y = 40…(2). On multiplying both the sides of the 2^nd equation by 5, we get 5x+5y = 200…(3). Now, on subtracting the 3^rd equation from the 1^st equation, we get 5x+8y-5x-5y = 245-200 or, 3y = 45 so that y = 45/3 = 15. Then, on substituting y = 15 in the 2^nd equation, we get x +15 = 40 so that x = 40-15 = 25. Thus, the the fuel efficiencies of the first car and and the second car that week were 15 miles/gallon and 25 miles per gallon respectively.