A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 2000 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

Question

A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 2000 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Let the two cars' distances be

first: x
second: y

Since mi/gal * gal = mi,
x + y= 2000
x/25 + y/40 = 65

Answer 2

To find out how many gallons of gas were consumed by each car, we can set up a system of equations based on the information provided.

Let's assume that the number of gallons consumed by the first car is x, and the number of gallons consumed by the second car is y.

According to the problem, the first car has a fuel efficiency of 25 miles per gallon, and the second car has a fuel efficiency of 40 miles per gallon.

So, we can set up the following equations:

Equation 1: x + y = 65 (total gas consumption for the week)
Equation 2: (25x) + (40y) = 2000 (total distance traveled by both cars)

To solve this system of equations, we can use the substitution or elimination method.

Let's use the substitution method:

From Equation 1, we can solve for x in terms of y:
x = 65 - y

Now, substitute this value of x into Equation 2:
25(65 - y) + 40y = 2000

Simplify the equation:
1625 - 25y + 40y = 2000
15y = 375
y = 25

Now, substitute the value of y back into Equation 1 to find x:
x + 25 = 65
x = 40

Therefore, the first car consumed 40 gallons of gas, and the second car consumed 25 gallons of gas during that week.