To determine how much farther Arianna's car can travel on one gallon of gas compared to Bo's car, we first need to calculate the gas mileage for both Arianna and Bo.
Bo's Gas Mileage: Bo uses 2 gallons of gas to drive 41.4 miles. To find his gas mileage in miles per gallon (mpg), we can use the formula:
\[ \text{Gas Mileage} = \frac{\text{Miles driven}}{\text{Gallons used}} = \frac{41.4 \text{ miles}}{2 \text{ gallons}} = 20.7 \text{ mpg} \]
Arianna's Gas Mileage: Next, we determine the gas mileage for Arianna's car based on the information in the table. We will calculate her gas mileage for each entry in the table by using the formula for gas mileage:
\[ \text{Gas Mileage} = \frac{\text{Miles driven}}{\text{Gallons used}} \]
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For \(x = 4\) gallons:
- \(y = 104.4\) miles \[ \text{Gas Mileage} = \frac{104.4}{4} = 26.1 \text{ mpg} \]
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For \(x = 10\) gallons:
- \(y = 261\) miles \[ \text{Gas Mileage} = \frac{261}{10} = 26.1 \text{ mpg} \]
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For \(x = 12\) gallons:
- \(y = 313.2\) miles \[ \text{Gas Mileage} = \frac{313.2}{12} = 26.1 \text{ mpg} \]
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For \(x = 14\) gallons:
- \(y = 365.4\) miles \[ \text{Gas Mileage} = \frac{365.4}{14} \approx 26.1 \text{ mpg} \]
From the calculations, we see that Arianna's car has a gas mileage of approximately 26.1 mpg.
Comparison:
To find how much farther Arianna's car can travel on one gallon of gas than Bo's, we subtract Bo's gas mileage from Arianna's gas mileage:
\[ \text{Difference} = \text{Arianna's mpg} - \text{Bo's mpg} = 26.1 - 20.7 = 5.4 \]
Thus, Arianna's car can travel 5.4 miles farther per gallon of gas than Bo's car.
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