A family had two cars. The first car fuel efficiency of 20 miles per gallon of gas and the second car has a fuel efficiency of 40 miles per gallon of gas. During one particular week the two cars went a combined Total of 1100 miles for a total gas consumption of 40 gallons how many gallons were consumed by each of the two cars that week?
Distance = (number of gallons)(rate in mpg)
let the number of gallons used by the gas-guzzler be x
then the number gallons used by the nice car = 40-x
20x + 40(40-x) = 1200
solve for x
Let's assume the number of gallons consumed by the first car is x.
Since the fuel efficiency of the first car is 20 miles per gallon, the total distance covered by the first car is x * 20.
The number of gallons consumed by the second car would be 40 - x, as the total consumption of both cars is 40 gallons.
Since the fuel efficiency of the second car is 40 miles per gallon, the total distance covered by the second car is (40 - x) * 40.
The sum of the distances covered by both cars is 1100 miles, so we can set up the equation:
x * 20 + (40 - x) * 40 = 1100
Simplifying the equation:
20x + (40 - x) * 40 = 1100
20x + 1600 - 40x = 1100
-20x + 1600 = 1100
-20x = 1100 - 1600
-20x = -500
x = -500 / -20
x = 25
Therefore, the first car consumed 25 gallons of gas, and the second car consumed 40 - 25 = 15 gallons of gas.
To find how many gallons were consumed by each of the two cars, we can set up a system of equations based on the information given.
Let's denote the number of gallons consumed by the first car as 'x' and the number of gallons consumed by the second car as 'y'.
According to the problem, the total distance covered by both cars is 1100 miles, and the total gas consumption is 40 gallons. We can express these relationships as equations:
Equation 1: x + y = 40 (Total gas consumption equation)
Equation 2: 20x + 40y = 1100 (Total distance equation)
Now, we can solve this system of equations to find the values of 'x' and 'y'.
To solve it, let's multiply Equation 1 by 20 to match the equation coefficients:
20x + 20y = 800
Now, subtract Equation 2 from this modified Equation 1 to eliminate 'x':
20x - 20x + 20y - 40y = 800 - 1100
-20y = -300
y = (-300)/(-20)
y = 15
Substitute the value of 'y' back into Equation 1 to find 'x':
x + 15 = 40
x = 40 - 15
x = 25
Therefore, the first car consumed 25 gallons, and the second car consumed 15 gallons during that week.
To summarize:
- The first car consumed 25 gallons of gas.
- The second car consumed 15 gallons of gas.