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The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car specifications that give fuel efficiency as 7.6 km per kilogram of fuel. Given that a mile is 1.609 km, a gallon is 3.785 liters, and a liter of gasoline has a mass of 0.729 kg, what is the car’s fuel efficiency in miles per gallon?

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JeanaShupp

Answer: [tex]4.5 \text{ miles per gallon}[/tex]

Step-by-step explanation:

Given :  The fuel efficiency of car = 7.6 km per kilogram

We also given that

1 mile = 1.609 km

Then, [tex]\text{1 km}=\dfrac{1}{0.609}\text{ mile}[/tex]

1 gallon = 3.785 liters

[tex]\text{1 liter}=\dfrac{1}{3.785}\text{ gallon}[/tex]

1 liter of gasoline = 0.729 kg

Then, [tex]\text{1 kg}=\dfrac{1}{0.729}\text{ liter}[/tex]

[tex]\Rightarrow\ \text{1 kg}=\dfrac{1}{0.729}\times\dfrac{1}{3.785}\text{gallon}[/tex]

Now, the fuel efficiency of car will be :

[tex]7.6\times\dfrac{1}{0.729}\times\dfrac{1}{3.785}\times\dfrac{1}{0.609}\\\\=4.52275317827\approx4.5 \text{ miles per gallon}[/tex]

Hence,  the car’s fuel efficiency in miles per gallon= 4.5

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