수학동아 - 폴리매스

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함께 풀고 싶은 문제

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[창의 퍼즐] 102등 기념 배기가스 문제

전자기역학 2020.04.04 00:41 조회 341

문제 푼 사람 1명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

자동차에서 나오는 배기가스는 심각한 오염을 일으킨다.

역학이는 차를 운전하며 차 뒤에 배기가스 필터를 설치해 최대한 배기가스를 막으려고 한다.(필터는 b만큼의 배기가스를 통과시킨다. 만약 b가 5/8이면 원래 배출되는 양의 5/8만큼 배출되는 것이다.)

만약 역학이가 배기가스 필터를 두 개 붙이면서 자동차를 a km/h의 속력으로 운전하면 배기가스가 1L가 나온다.

역학이가 배기가스 필터를 한 개 붙이면서 자동차를 9a km/h의 속력으로 운전하던 도중에 옆에서 전자기가 필터를 붙이지 않은 채로 a km/h로 차를 운전했을 때는 배기가스가 136L가 나온다.

그러면 a, b의 값은 각각 무엇인가?

(단, 배기가스는 1km/h당 1L가 나오고, 필터를 두 개를 붙였을 때에는 $b^{2}$ 만큼의 배기가스를 통과시킨다 한다.)

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