You are renting a car which is reported to achieve 11.9 km/L. How many miles will you be able to travel on 11.0 gallons of gasoline?
The correct answer and explanation is:
To solve this problem, we need to convert between units and apply the fuel efficiency correctly.
Step-by-Step Calculation
1. Convert the fuel efficiency to miles per gallon (mpg)
We are given:
- Fuel efficiency = 11.9 km/L
- 1 mile = 1.60934 kilometers
- 1 gallon = 3.78541 liters
We convert 11.9 km/L to miles per gallon (mpg): 11.9 km/L×(1 mile1.60934 km)×(3.78541 L1 gallon)11.9 \, \text{km/L} \times \left(\frac{1 \, \text{mile}}{1.60934 \, \text{km}}\right) \times \left(\frac{3.78541 \, \text{L}}{1 \, \text{gallon}}\right) =11.9×3.785411.60934≈11.9×2.35215≈27.9956 mpg= 11.9 \times \frac{3.78541}{1.60934} \approx 11.9 \times 2.35215 \approx 27.9956 \, \text{mpg}
So the car gets about 28.0 miles per gallon.
2. Calculate how many miles you can travel on 11.0 gallons
Distance=Fuel efficiency (mpg)×Gallons\text{Distance} = \text{Fuel efficiency (mpg)} \times \text{Gallons} =28.0 miles/gallon×11.0 gallons=308.0 miles= 28.0 \, \text{miles/gallon} \times 11.0 \, \text{gallons} = 308.0 \, \text{miles}
✅ Final Answer: 308.0 miles
Explanation (300 words)
To determine how far you can drive on a given amount of gasoline, you need to understand the relationship between fuel efficiency and fuel volume. In this problem, fuel efficiency is given in kilometers per liter (km/L), but the final result needs to be in miles, and fuel volume is provided in gallons. Therefore, we must convert both units of distance and volume.
First, convert the fuel efficiency from km/L to miles per gallon (mpg). This is done by multiplying the km/L value by the number of liters per gallon (3.78541 L/gallon) and dividing by the number of kilometers per mile (1.60934 km/mile). This tells you how many miles the car can travel using one gallon of gasoline.
Next, multiply the resulting mpg value by the number of gallons of fuel available—in this case, 11.0 gallons. This product gives you the total distance in miles that the car can travel on 11.0 gallons of fuel.
After performing the conversions and calculations, we find that a car with a fuel efficiency of 11.9 km/L can travel approximately 308 miles on 11 gallons of gasoline. This approach illustrates the importance of unit conversions when dealing with international measurements.