Question

A Toyota Prius hybrid gets 21 kilometers per liter in highway driving. What is the mileage in miles per gallon? (Given: \(1 \mathrm{~km}=0.621 \mathrm{mi}\) and \(1 \mathrm{~L}=0.264 \mathrm{gal})\).

Short answer

The mileage is approximately 49.32 miles per gallon.

Step-by-step solution

Convert Kilometers to Miles

First, we need to convert 21 kilometers to miles. We know that \(1 \text{ km} = 0.621 \text{ mi}\). Therefore, \(21 \text{ km} = 21 \times 0.621 \text{ mi} = 13.041 \text{ mi}\).

Convert Liters to Gallons

Next, we convert the 1 liter (used per 21 kilometers) to gallons. We know that \(1 \text{ L} = 0.264 \text{ gal}\). Therefore, \(1 \text{ L} = 0.264 \text{ gal}\).

Calculate Miles Per Gallon

Now, to find miles per gallon, divide the distance in miles by the volume in gallons. We have \(13.041 \text{ mi}\) and \(0.264 \text{ gal}\). Thus, the mileage is \(\frac{13.041 \text{ mi}}{0.264 \text{ gal}} \approx 49.32 \text{ mi/gal}\).

Key concepts

Metric to Imperial Conversion

When converting from metric units to imperial units, it's crucial to understand the relationships between these different measurements. Metric units, such as kilometers and liters, are widely used around the world, especially in scientific contexts. In this exercise, you're required to convert kilometers to miles and liters to gallons. Here are some common conversions:

• Distance: 1 kilometer is approximately equal to 0.621 miles.
• Volume: 1 liter is approximately equal to 0.264 gallons.

By applying these conversion factors, you can translate measurements from kilometers per liter (km/L) to miles per gallon (mi/gal). This process involves multiplying or dividing by the conversion factors to switch between the two systems.

Distance Conversion

Understanding how to convert distances from kilometers to miles is essential, especially in countries where the imperial system is predominant. To convert kilometers to miles, use the conversion factor where 1 kilometer equals 0.621 miles. Here’s how you can do it:

• Step 1: Take the number of kilometers you have.
• Step 2: Multiply that number by 0.621 to get the distance in miles.

For instance, converting 21 kilometers to miles involves multiplying 21 by 0.621, resulting in 13.041 miles. This allows you to work seamlessly across different measurement systems, ensuring accuracy and understanding.

Fuel Efficiency Calculation

Fuel efficiency is an important metric, especially when comparing the performance of vehicles across different regions. The fuel efficiency given in kilometers per liter (km/L) needs to be converted to miles per gallon (mi/gal) for better understanding in a region that uses the imperial system.

• Step 1: Convert the distance from kilometers to miles as previously explained.
• Step 2: Convert the volume from liters to gallons. For instance, 1 liter is 0.264 gallons.
• Step 3: Calculate miles per gallon by dividing the mileage in miles by the volume in gallons.

In this exercise, with 13.041 miles and 0.264 gallons, you divide to find roughly 49.32 miles per gallon. By understanding both the metric and imperial systems, you can assess fuel efficiency more accurately, regardless of your location.