(a). The fuel expense of the car in the complete trip in US dollars is \(\boxed{\$\,354}\).
(b). The fuel consumed in gallons per mile is \(\boxed{0.0254\text{ gallons/mile}}\).
Explanation:
Given:
The price of the fuel in Europe is \(1.063\text{ euros/ltr}\).
The amount of fuel required for every \(100\text{ km}\) is \(6.00\text{ ltr}\).
Part (A):
Concept:
The value of one euro equivalent to the US dollar is \(\$\,1.11\).
The cost of the fuel in terms of the US dollar is:
\(\begin{aligned}c&=1.063\text{ euros/ltr}\left(\dfrac{\$\,1.11}{1\text{ euro}}\right)\\&=\$\,1.18\text{ USD/ltr}\end{aligned}\)
Since the car consumes \(6\text{ ltr}\) of fuel during the journey of \(100\text{ km}\), the total fuel consumed by the car in the trip of \(5000\text{ km}\) is:
\(\begin{aligned}n&=\dfrac{6\text{ ltr}}{100\text{ km}}\times(5000\text{ km})\\&=300\text{ ltr}\end{aligned}\)
The fuel consumed by the car in the whole trip of \(5000\text{ km}\) is \(300\text{ ltr}\).
The fuel expense for the trip of \(5000\text{ km}\) can be obtained as:
\(\begin{aligned}\text{ cost}&=1.18\text{ USD/ltr}\times(300\text{ ltr})\\&=\$\,354\text{ USD}\end{aligned}\)
Thus, the price of the fuel of the car in the complete trip in US dollars is \(\boxed{\$\,354}\).
Part (B):
Concept:
The distance covered by the car in covering one mile is equivalent to \(1.61\text{ km}\).
The amount of fuel consumed by the car in covering one mile is:
\(\begin{aligned}v^{'}&=1.6\text{ km}\times\dfrac{6\text{ ltr}}{100\text{ km}}\\&=0.096\text{ ltr}\end{aligned}\)
The volume of oil consumed in terms of gallons per mile is:
\(\begin{aligned}v^{'}&=0.096\text{ ltr}\times\dfrac{1\text{ gallon}}{3.78\text{ ltr}}\\&=0.0254\text{ gallons}\end{aligned}\)
Thus, the fuel consumed in gallons per mile is \(\boxed{0.0254\text{ gallons/mile}}\).
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Units and Measurement
Keywords:
Rental package, car, average consumption, euro, US dollar, USD, europe, fuel on your trip, fuel cost, 6 liter, 1.063 euros/liter.
