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Home » New length = \( 15 + 0.2 \times 15 = 18 \, \textcm \) - ToelettAPP

New length = \( 15 + 0.2 \times 15 = 18 \, \textcm \) - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A geographer is analyzing data on coastal erosion and finds that the rate of erosion (in meters per year) for different coastal regions can be represented by a set of integers. If the greatest common divisor (GCD) of these rates for three regions is 6 and the total erosion rate for these regions over one year is 84 meters, what is the maximum possible erosion rate for any one region?

📌 Let the erosion rates for the three regions be \(6a\), \(6b\), and \(6c\), where \(\gcd(a, b, c) = 1\). The total erosion is given by:

📌 6a + 6b + 6c = 84

📌 Simplifying, we have:

📌 a + b + c = 14

📌 We aim to maximize one of \(6a\), \(6b\), or \(6c\). Without loss of generality, let’s maximize \(6a\). This implies maximizing \(a\) subject to \(a + b + c = 14\) and \(\gcd(a, b, c) = 1\).

📌 Start by examining possible values for \(a\):

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