To find the rate at which Lucy's car uses gas in miles per gallon, we need to calculate the miles per gallon based on the distance traveled and the amount of gas used.
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Convert the mixed number to an improper fraction: The distance traveled is \( 19 \frac{1}{2} \) miles. To convert this to an improper fraction: \[ 19 \frac{1}{2} = 19 + \frac{1}{2} = \frac{38}{2} + \frac{1}{2} = \frac{39}{2} \]
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Determine the amount of gas used: The car uses \(\frac{3}{4}\) of a gallon of gas.
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Calculate miles per gallon: Miles per gallon (mpg) can be calculated using the formula: \[ \text{mpg} = \frac{\text{miles traveled}}{\text{gallons used}} = \frac{\frac{39}{2}}{\frac{3}{4}} \]
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Dividing by a fraction: When you divide by a fraction, you multiply by its reciprocal: \[ \frac{\frac{39}{2}}{\frac{3}{4}} = \frac{39}{2} \times \frac{4}{3} \]
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Perform the multiplication: \[ = \frac{39 \times 4}{2 \times 3} = \frac{156}{6} \]
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Simplify the fraction: \[ = 26 \]
Thus, Lucy's car uses gas at a rate of 26 miles per gallon.