Question

Alex test drives four cars and records the distance traveled and the gallons of gas used in each case in the following table. Car Distance Driven (Miles) Gas Used (Gallons) A 102.3 11.5 B 78.1 7.9 C 57.8 6.2 D 142.9 15.9 Which car has the best gas mileage (miles per gallon)? (A) Car A (B) Car B (C) Car C (D) Car D

Short answer

The car with the best gas mileage is Car B, with the gas mileage of 9.9 miles per gallon (Answer choice B).

Step-by-step solution

Calculate the Gas Mileage for Each Car

We first need to calculate the gas mileage for each car. To calculate the gas mileage for each car, we need to divide the miles driven by the gallons of gas used. That is, Gas Mileage = (Distance Driven) / (Gas Used). (A) Gas Mileage for Car A: Gas Mileage = \( \frac{102.3}{11.5} = 8.9 \) miles per gallon (B) Gas Mileage for Car B: Gas Mileage = \( \frac{78.1}{7.9} = 9.9 \) miles per gallon (C) Gas Mileage for Car C: Gas Mileage = \( \frac{57.8}{6.2} = 9.3 \) miles per gallon (D) Gas Mileage for Car D: Gas Mileage = \( \frac{142.9}{15.9} = 9.0 \) miles per gallon

Compare the Gas Mileage of Each Car

Now, compare the gas mileage of each car by checking which car has the highest gas mileage. We can see from above calculations, Car A - 8.9 miles per gallon Car B - 9.9 miles per gallon Car C - 9.3 miles per gallon Car D - 9.0 miles per gallon Car B has the highest gas mileage at 9.9 miles per gallon.

Answer: Car With the Best Gas Mileage

The car with the best gas mileage is Car B, with the gas mileage of 9.9 miles per gallon (Answer choice B).

Key concepts

Gas Mileage Calculation

Calculating gas mileage is an essential skill when assessing the efficiency of a vehicle in terms of fuel consumption. To determine a car's gas mileage, you divide the distance it traveled by the amount of gas it used. This calculation gives you the number of miles the car can travel on one gallon of gasoline, which is typically measured in miles per gallon (mpg). For example, if a car drives 102.3 miles while using 11.5 gallons of gas, its gas mileage can be calculated using the formula:\[\text{Gas Mileage} = \frac{102.3 \text{ miles}}{11.5 \text{ gallons}} = 8.9 \text{ mpg}.\]This straightforward computation provides a clear figure that tells you how fuel-efficient the car is. A higher mpg indicates better fuel efficiency, which is often desirable for cost savings and environmental considerations.

Distance and Rate Problems

Understanding distance and rate problems is crucial in many real-world scenarios, such as calculating travel time, route planning, and assessing vehicle efficiency. These problems involve three main components: distance, rate (speed), and time. The basic relationship between these components is given by the formula:\[\text{Distance} = \text{Rate} \times \text{Time}.\]In the context of our exercise, we've focused on distance and rate (which here is synonymous with speed or gas mileage), where rate is derived from dividing distance by the amount of fuel used. Recognizing the importance of each factor allows you to solve problems efficiently. For instance, if you know two of the quantities (distance and gas used), you can easily calculate the third (mileage or rate).Furthermore, understanding this relationship helps you analyze varied travel scenarios, such as comparing trips in different cars to see which is more efficient. This means that whenever you are provided with two of these pieces, the third can be straightforwardly calculated to facilitate decision-making about travel or fuel usage.

Analytical Comparison

Comparative analysis is a technique used to evaluate and distinguish options. It involves comparing different metrics to determine which is superior based on criteria established by the user. In our exercise, once we calculated the gas mileage for each vehicle, a simple comparative analysis enabled us to determine the most fuel-efficient car. Here's how such a comparison works in practice:

• First, ensure that you have consistent data for each option (in this case, the gas mileage for each car).
• Next, line up the data to compare directly; for example, list the mpg values of each car side by side.
• Finally, identify the highest value, which indicates the best performance under that criterion.

By systematically applying this method, you can effectively compare options like vehicles, travel routes, or even different products. This skill is invaluable as it allows for data-driven decision-making, ensuring the choice made is based on clear, quantifiable metrics, leading to better outcomes in various scenarios.