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2014 AMC 10B Problem 8

Problem 8 of 25EasierAlgebra

A truck travels b6\dfrac{b}{6} feet every tt seconds. There are 33 feet in a yard. How many yards does the truck travel in 33 minutes?

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Solution

This means it travels b18\dfrac{b}{18} yards in tt seconds since a yard is 33 feet. Then, in one second, it travels b18t\dfrac{b}{18t} yards. Therefore, in 33 minutes which is 180180 seconds, it travels b18t⋅180=10bt.\dfrac{b}{18t}\cdot 180 = \dfrac {10b}t. Thus, the correct answer is E .

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Concepts: unit conversion · rate

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.