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A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If you are driving this car in Europe and want to compare its mileage with that of other European cars, express this mileage in km/L (L = liter). Use the conversion factors in Appendix E. (b) If this car’s gas tank holds 45 L, how many tanks of gas will you use to drive 1500 km?

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We will start by defining the units and their respective equivalences between the proposed measurement systems

[tex]1km = 0.6214mi[/tex]

[tex]1gallon = 3.788 litres[/tex]

PART A ) The mileage of the car is 55mpg (Miles per gallon)

[tex]55mpg = 55(\frac{miles}{gallon}) (\frac{1km}{0.6214miles})(\frac{1gallon}{3.788L})[/tex]

[tex]55mpg = 23.4km/L[/tex]

Therefore the mileage of the car is 23.4km/L

PART B ) The mileage of the car means that the car travels 23.4km and consumes 1 liter of fuel. Then

[tex]1L = 23.4km[/tex]

For the car to travel 1500km the amount of fuel would be,

[tex]1500km= (1500km)(\frac{1L}{23.4km})[/tex]

[tex]1500km = 64.1L[/tex]

But 1 gas tank can only hold 45Liters of fuel, then the number of tank required would be

[tex]\text{Number of tanks required} = \frac{64.1L}{45L}[/tex]

[tex]\text{Number of tanks required} = 1.4tanks[/tex]

Thus the number of tanks of gas required to drive 1500km is 1.4

xero099

a) The car have an equivalent European mileage of 25.284 kilometres per liter.

b) Up to 2 tanks of gas are needed to drive 1500 kilometers.

Fuel efficiency analysis of a vehicle

a) Dimensionally speaking, the gasoline mileage is distance (miles) divided by volume (gallon). Additionally, a gallon equals 3.5 liters and a mile equals 1,609 kilometers. Hence, we make the following conversion to determine the equivalent European mileage:

[tex]x = 55\,\frac{mi}{gal} \times \frac{1\,gal }{3.5\,L} \times \frac{1.609\,km}{1\,mi}[/tex]

[tex]x = 25.284\,\frac{km}{L}[/tex]

The car have an equivalent European mileage of 25.284 kilometres per liter. [tex]\blacksquare[/tex]

b) The number of tanks of gas ([tex]n[/tex]) needed to drive a given distance is represented by the following formula:

[tex]n = \frac{s}{c\cdot r}[/tex] (1)

Where:

  • [tex]s[/tex] - Travelled distance, in kilometres.
  • [tex]c[/tex] - Capacity of the tank of gas, in liters.
  • [tex]r[/tex] - European mileage, in kilometres per gallon.

Now we proceed to calculate the amount of tanks: ([tex]s = 1500\,km[/tex], [tex]c = 45\,L[/tex], [tex]r = 25.284\,\frac{km}{L}[/tex])

[tex]n = \frac{1500\,km}{(45\,L)\cdot (25.284\,\frac{km}{L} )}[/tex]

[tex]n = 1.318[/tex]

Up to 2 tanks of gas are needed to drive 1500 kilometers. [tex]\blacksquare[/tex]

To learn more on mileages, we kindly invite to check this verified question: https://brainly.com/question/4564001

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