2014 AMC 10B Problem 8 — Solution | LIVE by Po-Shen Loh

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2014 AMC 10B Problem 8

Attempt Problem 8 of the 2014 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

A truck travels $\dfrac{b}{6}$ feet every $t$ seconds. There are $3$ feet in a yard. How many yards does the truck travel in $3$ minutes?

$\dfrac{b}{1080t}$

$\dfrac{30t}{b}$

$\dfrac{30b}{t}$

$\dfrac{10t}{b}$

$\dfrac{10b}{t}$

Answer: E

Concepts:unit conversion rate

Difficulty rating: 960

Solution:

This means it travels $\dfrac{b}{18}$ yards in $t$ seconds since a yard is $3$ feet. Then, in one second, it travels $\dfrac{b}{18t}$ yards.

Therefore, in $3$ minutes which is $180$ seconds, it travels $\dfrac{b}{18t}\cdot 180 = \dfrac {10b}t.$

Thus, the correct answer is E .

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