You and your friends are organizing a trip to Europe. Your plan is to rent a car and drive through the major European capitals. By consulting a map you estimate that you will cover a total distance of 5000 \rm km. Consider the euro-dollar exchange rate given in the introduction and use dimensional analysis to work through these simple problems.You select a rental package that includes a car with an average consumption of 6.00 \rm liters of fuel per 100 \rm km. Considering that in Europe the average fuel cost is 1.063 \rm euros/ liter.How many gallons of fuel would the rental car consume per mile?
You have a lot of numbers and information you don't need. All you have to do is convert 6.00 liters/100 km (which is 16.67 km/liter) to miles per gallon. I assume you know how to do that. There are 3.785 liters in a gallon and 1.609 km in a mile.
cry
To find the number of gallons of fuel the rental car would consume per mile, we need to first convert the given consumption rate from liters per 100 km to gallons per mile.
Step 1: Convert liters per 100 km to liters per 1 km
Since the consumption rate is given as 6.00 liters of fuel per 100 km, we can write it as:
6.00 liters / 100 km
To convert this to liters per 1 km, we divide both the numerator and denominator by 100:
(6.00 liters / 100 km) = (0.06 liters / 1 km)
Step 2: Convert liters per 1 km to gallons per 1 km
To convert liters to gallons, we need to know the conversion factor. In this case, we'll use the fact that 1 gallon is equal to approximately 3.78541 liters.
So, to convert from liters to gallons, we divide the liters by the conversion factor:
(0.06 liters / 1 km) * (1 gallon / 3.78541 liters) = (0.06 / 3.78541) gallons / km
Step 3: Convert gallons per km to gallons per mile
To convert kilometers to miles, we need to know the conversion factor. The conversion factor is approximately 0.621371.
So, to convert from kilometers to miles, we multiply the kilometers by the conversion factor:
(0.06 / 3.78541) gallons / km * (1 km / 0.621371 miles) = (0.06 / 3.78541 / 0.621371) gallons / mile
Now we can calculate the number of gallons of fuel the rental car would consume per mile:
(0.06 / 3.78541 / 0.621371) gallons / mile ≈ 0.0254 gallons / mile
Therefore, the rental car would consume approximately 0.0254 gallons of fuel per mile.
To find out how many gallons of fuel the rental car would consume per mile, we need to convert the given values to the appropriate units.
First, let's convert the distance from kilometers to miles. Since there are approximately 0.621 miles in 1 kilometer, we can calculate the distance in miles:
Distance in miles = 5000 km * 0.621 miles/km
Distance in miles = 3105 miles
Next, let's convert the fuel consumption from liters per 100 km to gallons per mile. To do this, we'll need to convert liters to gallons and kilometers to miles:
Fuel consumption in gallons per mile = (6.00 liters/100 km) * (1 gallon/3.785 liters) * (0.621 miles/km)
Fuel consumption in gallons per mile ≈ 0.101 gallons/mile
Therefore, the rental car would consume approximately 0.101 gallons of fuel per mile on this trip through major European capitals.