2014 AMC 10B Problems/Problem 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?

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


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.





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 $\boxed{\text{(E)}}$



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See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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All AMC 10 Problems and Solutions

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