2022 AMC 10A Problems/Problem 4
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[hide]Problem
In some countries, automobile fuel efficiency is measured in liters per kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals miles, and gallon equals liters. Which of the following gives the fuel efficiency in liters per kilometers for a car that gets miles per gallon?
Solution 1
The formula for fuel efficiency is Note that mile equals kilometers. We have Therefore, the answer is
~MRENTHUSIASM
Solution 2
Since it can be a bit odd to think of "liters per km", this statement's numerical value is equivalent to km per liter:
km requires liters, so the numerator is simply . Since liters is gallon, and miles is gallon, we have .
Therefore, the requested expression is -Benedict T (countmath1)
Solution 3
A car that gets a gallon for miles has a fuel efficiency of We want to convert these units to liters and kilometers. Since one gallon is liters, that can be rewritten as .
Now to convert the miles into kilometers. km is miles, so mile is km. Plug that in to get Simplifying, we get .
But the problem asked for the fuel efficiency of liters per km, not just km. So instead of , we put in , getting as the answer.
~mihikamishra
Video Solution 1 (Quick and Easy)
~Education, the Study of Everything
Video Solution 2
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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