Question

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?

$\ 60$

$\ 80$

$\ 100$

$\ 120$

$\ 140$

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Written solution:

Converting $2$ minutes and $45$ seconds into seconds, we get $2 \cdot 60 + 45 = 165$ seconds. Since $6$ cars passed in $10$ seconds, at the same rate the number of cars $x$ passing in $165$ seconds satisfies $\dfrac{6}{10}=\dfrac{x}{165}.$

Solving gives $x=\dfrac{165\cdot6}{10}=99.$ The closest answer choice is $100$ .

Thus, C is the correct answer.

2013 AMC 8 Problem 7

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Problem 7 in Other Years