Question

A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 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 x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 65-x (since the total gas consumption is 65 gallons).

Using the formula distance = fuel efficiency x gas consumption, we can set up two equations:

First car: distance = 30x

Second car: distance = 20(65-x)

Since the total distance is 1700 miles, we can set up another equation:

Total distance: 30x + 20(65-x) = 1700

Simplifying this equation, we get:

30x + 1300 - 20x = 1700

10x = 400

x = 40

Therefore, the first car consumed 40 gallons and the second car consumed 65-40 = 25 gallons.

Answer 2

Let's assume that the first car traveled x miles and the second car traveled y miles during that week. We can set up two equations based on the given information:

x + y = 1700 (the combined total of miles traveled by both cars)

x/30 + y/20 = 65 (the total gas consumption)

To solve for x and y, we can use the first equation to express one variable in terms of the other. For example, we can solve for y as follows:

y = 1700 - x

Substituting this into the second equation, we get:

x/30 + (1700 - x)/20 = 65

Multiplying both sides by the common denominator 60, we can simplify the equation:

2x + 3(1700 - x) = 3900

2x + 5100 - 3x = 3900

-x = -1200

x = 1200

So the first car traveled 1200 miles during the week. We can use this value to find the second car's mileage:

y = 1700 - x = 1700 - 1200 = 500

Therefore, the second car traveled 500 miles during the week. To find the gallons of gas consumed by each car, we can use the fuel efficiency rates:

Gallons used by first car = 1200 miles / 30 mpg = 40 gallons

Gallons used by second car = 500 miles / 20 mpg = 25 gallons

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