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

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2014 AMC 10B Problem 8

Below is the professionally curated solution for Problem 8 of the 2014 AMC 10B, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:unit conversion rate

Difficulty rating: 960

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?

$\dfrac{b}{1080t}$

$\dfrac{30t}{b}$

$\dfrac{30b}{t}$

$\dfrac{10t}{b}$

$\dfrac{10b}{t}$

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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