A car drove 148 miles using 4 gallons of gasoline. How many gallons will it take to drive 9 1/4 miles?
The Correct Answer and Explanation is:
To find how many gallons of gasoline it will take to drive 9¼ miles, use the concept of unit rate or proportional reasoning. First, determine the rate of gasoline consumption in miles per gallon, then use this rate to find how many gallons are needed for a smaller distance.
Step 1: Find the miles per gallon rate
The car drove 148 miles using 4 gallons.
To find miles per gallon: 148 miles4 gallons=37 miles per gallon\frac{148 \text{ miles}}{4 \text{ gallons}} = 37 \text{ miles per gallon}4 gallons148 miles=37 miles per gallon
This means the car drives 37 miles on one gallon of gasoline.
Step 2: Convert 9¼ miles to an improper fraction
914=374 miles9\frac{1}{4} = \frac{37}{4} \text{ miles}941=437 miles
Step 3: Use the rate to find gallons needed
To find how many gallons are needed to drive 374\frac{37}{4}437 miles, divide the number of miles by the miles per gallon: 37437=374×137=14 gallons\frac{\frac{37}{4}}{37} = \frac{37}{4} \times \frac{1}{37} = \frac{1}{4} \text{ gallons}37437=437×371=41 gallons
✅ Final Answer:
14 gallon or 0.25 gallon\boxed{\frac{1}{4} \text{ gallon or 0.25 gallon}}41 gallon or 0.25 gallon
Explanation :
When solving real-life problems involving fuel usage, understanding the relationship between distance traveled and the amount of fuel consumed is essential. This type of problem relies on proportional reasoning. If a car uses a fixed amount of fuel to travel a certain distance, then for any other distance, the fuel used will be in direct proportion.
In this problem, the car drives 148 miles using 4 gallons of gasoline. To determine the fuel efficiency, divide the distance by the gallons used: 148 miles4 gallons=37 miles per gallon\frac{148 \text{ miles}}{4 \text{ gallons}} = 37 \text{ miles per gallon}4 gallons148 miles=37 miles per gallon
This tells us that each gallon of gasoline allows the car to travel 37 miles. Now, to determine how much gasoline the car needs to travel 9¼ miles, express 9¼ as an improper fraction: 914=3749\frac{1}{4} = \frac{37}{4}941=437. To find the number of gallons required, divide the miles to be traveled by the miles the car can go per gallon: 37437=14 gallon\frac{\frac{37}{4}}{37} = \frac{1}{4} \text{ gallon}37437=41 gallon
This means that to travel 9¼ miles, the car will use only one-quarter of a gallon. This approach ensures accuracy by using consistent units and mathematical operations. Understanding this method helps in many situations, like estimating fuel costs, planning trips, or analyzing vehicle efficiency.
