Learning Goal: To understand how to use unit conversion to solve problems. Unit

Question

Learning Goal: To understand how to use unit conversion to solve problems. Unit conversion is not limited to physics problems but is part of our everyday life, correct use of conversion factors is essential to working through problems of practical importance. For example, unit conversion could be used in problems involving currency exchange. Say you want to calculate how many euros you got if you exchange 3600 us dollars. (USD), given the exchange rate 1 EUR = 1.20 USD, that is, 1 euro to 1 20 us dollars. Begin by writing down the starting value. 3600 USD. This can also be written as a fraction: Next, convert dollars to euros. This conversion involves multiplying by a simple conversion factor derived from the exchange rate: Note that the "dollar" unit, USD. should appear on the bottom of this conversion factor, since USD appears on the top of the starting value. Finally, since dollars are divided by dollars, the units can be canceled and the final result is Currency exchange is only one example of many practical situations where unit conversion may help you to work through problems. Remember that unit conversion involves multiplying a given value by a conversion factor, resulting in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. 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 km. Consider the euro-dollar exchange rate given in the introduction and use unit conversion to work through these simple problems. You select a rental package that includes a car with an average consumption of 6.00 liters of fuel per 100 km. Considering that in Europe the average fuel cost is 1.063 euros/liter, how much (in US dollars) will you spend in fuel on your trip? Express your answer numerically in US dollars to three significant figures. How many gallons of fuel would the rental car consume per mile? Express your answer numerically in gallons per mile to three significant figures.

Explanation / Answer

the total trip is 5000 km,

car average consumption of fuel is 6 lts per 100 km,so for 5000 km the fuel cosumption is
           5000*6/100 = 300 lts

now exchange rate is 1 EUR = 1.2 USD
Part A

AVERAGE fuel cost per lt in Europe is 1.063 EUR = 1.063*1.2 = 1.2756 USD

now the cost of 300 lts of fuel is 300*1.2756 = 382.680 USD

Part B

total trip is 5000 km , fuel consumed is 300 lts
converting km in ot miles total trip in miles = 3106.856

fuel consumption per 100 km is 6 lts, that is 62.1371 miles -------------> 6 lts

now fuel consumption per 1 mile is = 0.096560 lts
converting lts in to gallons 1 lt = 0.26417 gallons then 0.096560 lts = 0.025508 gallon

The rentral car can consume 0.025508 gallon per mile.

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