AMC 10 · 2014 · #8
Grade 6 arithmeticPick an answer.
AMC 10 2014 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The problem mixes feet with yards and seconds with minutes, so tracking units is the backbone: line every quantity up in one unit, then multiply and divide. The letters b and t are carried along as an algebraic expression, and the answer choices let you sanity-check by where b and t land.
Convert minutes to seconds
The rate is measured per t seconds but the trip is given in minutes, so match them: 3 × 60 = 180 seconds.
You can only combine quantities once they share the same unit.
6.RP.A.3Analyze The UnitsTotal the feet traveled
Each t-second chunk covers feet and 180 s holds chunks, so the feet total .
Total distance is how many equal chunks you travel times the length of one chunk.
6.RP.A.2Analyze The UnitsSimplify the feet expression
Reduce 180 over 6 — letters obey the same rules as numbers — leaving feet.
Simplifying an expression with letters works the same as with plain numbers.
6.EE.A.2Analyze The UnitsConvert feet to yards
A yard is 3 feet, so divide by 3: ÷ 3 = yards, choice (E).
It takes more feet to make each yard, so the yard count is smaller — you divide.
It takes more feet to make each yard, so the yard count is smaller and you divide.
▸ Why?
A yard is one fixed bundle of feet, so counting yards is counting how many bundles fit.
▸ Why?
Dividing undoes the multiplying that built the feet, so it walks back to the yards.
Get everything into the same units first, and then the multiplying and dividing takes care of itself.
- Convert minutes to seconds
- Total the feet traveled
- Simplify the feet expression
- Convert feet to yards