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 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1225 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?Note that the ALEKS graphing calculator can be used to make computations easier.Firstcar:gallonsSecondcar:gallons
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 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1225 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?Note that the ALEKS graphing calculator can be used to make computations easier.Firstcar:gallonsSecondcar:gallons
Solution
To solve this problem, we can set up a system of two equations based on the information given.
Let's denote: X = the number of gallons consumed by the first car Y = the number of gallons consumed by the second car
From the problem, we know two things:
-
The total distance covered by both cars is 1225 miles. Since distance = rate * time, and in this case, 'time' is the amount of fuel consumed, we can write this as: 25X + 15Y = 1225
-
The total fuel consumed by both cars is 65 gallons. So, we can write this as: X + Y = 65
Now we have a system of two equations, and we can solve it step by step.
First, let's isolate Y in the second equation: Y = 65 - X
Now, substitute Y in the first equation: 25X + 15(65 - X) = 1225 25X + 975 - 15X = 1225 10X = 250 X = 25
Substitute X = 25 in the equation Y = 65 - X: Y = 65 - 25 Y = 40
So, the first car consumed 25 gallons and the second car consumed 40 gallons.
Similar Questions
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 23 gallons of gasoline to travel 460 miles. If the car travels 240 miles, how much gasoline does it need?gallons
A family is going on a road trip for their summer vacation. They plan their trip, including travel distances, fuel costs, and food expenses. They plan to travel a total distance of 450.5 km. On the first day, they travel 175.25 km, and on the second day, they travel 198.75 km. How many kilometers are left for them to travel?The car consumes fuel at a rate of 0.08 liters per kilometer. How much fuel will they need for the remaining distance?
Martina drove 250 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 275 miles? gallons
Aaron's dad has a pickup truck and his mom has an SUV. Last week, his dad traveled 84 miles in the pickup truck on 4 gallons of gas. His mom traveled 72 miles in the SUV on 3 gallons of gas. How many more miles per gallon did the SUV get than the truck?
A car travels 150 miles using 5 gallons of fuel. How many gallons are needed to travel 450 miles?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.