You plan to take a 2000-mile trip in your car, which averages 32 miles per gallon. How many gallons of gasoline should you expect to use? would a car that has only half the gas mileage (16 miles per gallon) require twice as much gasoline for the same trip? Explain
The correct answer and explanation is :
For the 2000-mile trip, a car that averages 32 miles per gallon will require 62.5 gallons of gasoline. If the car has half the gas mileage (16 miles per gallon), it will need 125 gallons of gasoline for the same trip.
Now, regarding the second part of your question: a car with half the gas mileage (16 miles per gallon) will indeed require twice as much gasoline for the same trip. This can be understood by considering how fuel efficiency works.
The relationship between the distance traveled, fuel consumption, and gas mileage is inversely proportional. In simple terms, the less efficient a car is in terms of miles per gallon (mpg), the more fuel it needs to travel the same distance. When the car’s mpg is halved, the number of gallons required for a fixed distance (2000 miles in this case) doubles. This is because for every mile traveled, the car consumes more fuel.
Example Breakdown:
- At 32 mpg, the car consumes 1 gallon of gasoline every 32 miles.
- At 16 mpg, the car consumes 1 gallon of gasoline every 16 miles.
For the same 2000-mile trip, the first car uses 62.5 gallons, while the second car, with half the mileage, uses 125 gallons. This demonstrates that with half the gas mileage, the car requires exactly twice the fuel.
Here is the bar graph comparing the gasoline required for the two cars over the 2000-mile trip. As you can see, the car with 32 miles per gallon requires 62.5 gallons, while the car with 16 miles per gallon requires 125 gallons, showing that the car with half the mileage indeed requires twice the fuel.