Problem 7 · 2013 AMC 8
Easy
Ratios, Rates & Proportions
proportion
Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?
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Answer: C — About 100 cars.
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Hint 1 of 2
Constant speed means the cars-per-second rate never changes. So the whole train is just the early sample (6 cars in 10 s) scaled up to the full time. Find that one rate first.
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Hint 2 of 2
Turn the count into a rate (cars per second), then multiply by the total seconds. "Constant speed" is the green light to use a single proportion.
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Approach: scale the cars-per-second rate to the total time
- Get everything in one unit: total time = 2 × 60 + 45 = 165 seconds.
- The rate is 6 cars every 10 seconds = 0.6 cars/second, and it holds the whole time. So cars = 0.6 × 165 = 99.
- The answer choices are round numbers, so 99 → 100 — "most likely" signals you to round to the nearest choice.
- Sanity check: 165 s is about 16 ten-second chunks of 6 cars ≈ 16 × 6 ≈ 96, comfortably near 100.
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