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2014 AMC 10B Problem 8

2014 AMC 10B Problem 8AMC 10 Step by Step

Name: Date: September 13, 2026

Linear Equations & Word Problems · difficulty 2 of 5 · about 2 min · position P1-10

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

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

Answer

Key insight

Convert to a rate of b/(6t) feet per second, multiply by 180 seconds, then divide by 3 for yards.

Solution

The truck's speed is $\frac{b/6}{t} = \frac{b}{6t}$ feet per second.

Three minutes is $180$ seconds, so in that time it covers
$\frac{b}{6t} \cdot 180 = \frac{30b}{t} \text{ feet}.$

Since $3$ feet make a yard, that is $\frac{30b}{t} \div 3 = \frac{10b}{t}$ yards.

The answer is $\boxed{\textbf{(E)}\ \frac{10b}{t}}$ .

Why this works

Every rate problem is distance $=$ rate $\times$ time once all units match. Convert the time to seconds first (to match the rate), then convert the result to the requested unit. A quick sanity check: more time or a larger $b$ should mean more yards, and a larger $t$ fewer, which rules out choices (B) and (D) immediately.

Alternative approach

Plug in $b = 6$ , $t = 1$ : the truck travels $1$ foot per second, so $180$ feet in $3$ minutes, or $60$ yards. Only $\frac{10b}{t} = 60$ matches.

The trap

Forgetting one of the two conversions (minutes to seconds, feet to yards) or dividing by 3 twice, producing 30b/t or 10b/(3t).

Common mistakes

Forgetting one of the two conversions (minutes to seconds, feet to yards) or dividing by 3 twice, producing 30b/t or 10b/(3t).
Inverting the rate (seconds per foot) and getting $t$ in the numerator.

Techniques

Set up the equation/formula and compute; no special trick needed · Test small/specific values or special cases to find or verify the answer