To find out how much farther Daniel's car can travel on one gallon of gas compared to Bo's car, we need to derive the distance per gallon for both cars.
Step 1: Calculate Bo's car's miles per gallon.
Bo drives 256.5 miles using 9 gallons of gas. The miles per gallon (MPG) for Bo's car can be calculated as:
\[ \text{MPG}_\text{Bo} = \frac{\text{miles driven}}{\text{gallons used}} = \frac{256.5 \text{ miles}}{9 \text{ gallons}} \]
Calculating this:
\[ \text{MPG}_\text{Bo} = \frac{256.5}{9} \approx 28.5 \text{ miles per gallon} \]
Step 2: Determine Daniel's car miles per gallon using the given equation.
The equation provided for Daniel is:
\[ y = 31.5x \]
where \(y\) represents the number of miles Daniel can drive for \(x\) gallons of gas. To find the miles per gallon, we can compute \(y\) when \(x = 1\):
\[ y = 31.5 \times 1 = 31.5 \text{ miles} \]
Thus, Daniel's car can travel 31.5 miles on one gallon of gas.
Step 3: Calculate the difference in mileage per gallon between Daniel's and Bo's cars.
Now we find the difference between the distances per gallon for Daniel's and Bo's cars:
\[ \text{Difference} = \text{MPG}\text{Daniel} - \text{MPG}\text{Bo} = 31.5 - 28.5 \]
Calculating this:
\[ \text{Difference} = 31.5 - 28.5 = 3 \text{ miles} \]
Thus, Daniel's car can travel 3 miles farther on one gallon of gas than Bo's car.
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