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2x + 4y = 32.00 - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A train travels from City A to City B at 60 km/h and returns at 90 km/h. If the total travel time is 5 hours, find the distance between the two cities.

📌 Let the distance be \( d \).

📌 Time from A to B is \( \frac{d}{60} \) hours, and return time is \( \frac{d}{90} \) hours.

📌 Total time: \( \frac{d}{60} + \frac{d}{90} = 5 \).

📌 Solve: \( \frac{3d + 2d}{180} = 5 \) gives \( 5d = 900 \), so \( d = 180 \) km.

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the first term is 3 and the common difference is 2, find \( n \) such that \( S_n = 210 \).

📌 Substitute: \( 210 = \frac{n}{2}(2 \times 3 + (n-1) \times 2) = \frac{n}{2}(6 + 2n - 2) = \frac{n}{2}(2n + 4) \).

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