Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.3 AIME Find the answer Italy

Problem:

Andrea, traveling on a tram, passes Mafalda who is walking on the same road in the opposite direction. After 10 seconds he gets off the tram and chases after her. Knowing that Andrea's walking speed is twice that of Mafalda and one fifth of that of the tram, how many seconds does it take him to reach his friend from the moment he gets off?

Pick one

Solution

Solution:

The answer is (D). If Mafalda's speed is $v$ meters/second, we know that Andrea's is $2v$ meters/second and the tram's is $10v$ meters/second. When Andrea gets off the tram, his distance from Mafalda is therefore $10v$ meters $+ 10 \times 10v$ meters $= 110v$ meters. Since his speed is twice that of Mafalda, in chasing after her he will approach her at a speed equal to $v$ meters/second; therefore he will take 110 seconds.

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