To determine how much farther Genesis's car can travel on one gallon of gas compared to Aisha's car, we first need to calculate the miles per gallon (mpg) for each of them based on the data provided.
Aisha's Car
From the graph data for Aisha:
- At \( x = 5 \) gallons, \( y = 93 \) miles.
- At \( x = 10 \) gallons, \( y = 186 \) miles.
To find Aisha's miles per gallon:
- Calculate the miles per gallon using the points provided.
- From \( (5, 93) \): \[ \text{MPG} = \frac{93 \text{ miles}}{5 \text{ gallons}} = 18.6 \text{ miles per gallon} \]
- From \( (10, 186) \): \[ \text{MPG} = \frac{186 \text{ miles}}{10 \text{ gallons}} = 18.6 \text{ miles per gallon} \]
So, Aisha's car offers a mileage of 18.6 miles per gallon.
Genesis's Car
Now, we look at Genesis's mileage from the table:
- At \( x = 3 \) gallons, \( y = 77.4 \) miles.
- At \( x = 5 \) gallons, \( y = 129 \) miles.
- At \( x = 10 \) gallons, \( y = 258 \) miles.
- At \( x = 14 \) gallons, \( y = 361.2 \) miles.
To find Genesis's miles per gallon:
- Calculate the miles per gallon using the points provided.
- From \( (3, 77.4) \): \[ \text{MPG} = \frac{77.4 \text{ miles}}{3 \text{ gallons}} \approx 25.8 \text{ miles per gallon} \]
- From \( (5, 129) \): \[ \text{MPG} = \frac{129 \text{ miles}}{5 \text{ gallons}} = 25.8 \text{ miles per gallon} \]
- From \( (10, 258) \): \[ \text{MPG} = \frac{258 \text{ miles}}{10 \text{ gallons}} = 25.8 \text{ miles per gallon} \]
- From \( (14, 361.2) \): \[ \text{MPG} = \frac{361.2 \text{ miles}}{14 \text{ gallons}} \approx 25.8 \text{ miles per gallon} \]
So, Genesis's car offers a mileage of 25.8 miles per gallon.
Conclusion
Now, to find how much farther Genesis's car can travel on one gallon of gas compared to Aisha's car, we subtract Aisha's mpg from Genesis's mpg: \[ \text{Difference} = 25.8 \text{ mpg} - 18.6 \text{ mpg} = 7.2 \text{ miles per gallon} \] Thus, Genesis's car can travel 7.2 miles farther per gallon of gas than Aisha's car.
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