2014 AMC 10B Problems/Problem 8

Problem

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?

$\textbf {(A) } \frac{b}{1080t} \qquad \textbf {(B) } \frac{30t}{b} \qquad \textbf {(C) } \frac{30b}{t}\qquad \textbf {(D) } \frac{10t}{b} \qquad \textbf {(E) } \frac{10b}{t}$

Solution

Converting feet to yards and minutes to second, we see that the truck travels $\dfrac{b}{18}$ yards every $t$ seconds for $180$ seconds. We see that he does $\dfrac{180}{t}$ cycles of $\dfrac{b}{18}$ yards. Multiplying, we get $\dfrac{180b}{18t}$ , or $\dfrac{10b}{t}$ , or $\boxed{\textbf{(E)}}$ .

Solution 2

We set a proportion by letting the $x$ being the number of feet the truck travels in $3$ minutes.

$\frac{\frac{b}{6}}{t}=\frac{x}{180}$

$\frac{b}{6t}=\frac{x}{180}$

$\frac{180b}{6t}=x$

$x=\frac{30b}{t}$

Remember $x$ is the number of feet the truck travels, so we divide by $3$ to convert to yards.

$\frac{x}{3}=\frac{10b}{t}$ , which corresponds to $\boxed{\text{(E)}}$

Video Solution (CREATIVE THINKING)

https://youtu.be/wSRcdsCzyJE

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Video Solution

https://youtu.be/j5pWLnlQkwE

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2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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