Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.4 AIME Find the answer Italy

Problem:

A train 500 meters long crosses at constant speed a tunnel 3 kilometers long. Knowing that 50 seconds have passed from the moment in which the last carriage of the train entered the tunnel to when the locomotive emerges from the other exit, it can be stated that the speed of the train is:

Pick one

Solution

Solution:

The answer is $(\mathbf{E})$ . In 50 seconds the locomotive of the train travels $3-0,5=2,5$ kilometers. Therefore its speed is
$\frac{2,5}{50} \mathrm{~km} / \mathrm{s}=0,05 \cdot 3600 \mathrm{~km} / \mathrm{h}=180 \mathrm{~km} / \mathrm{h} .$

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.