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Home » Since $\cos 60^\circ = \frac12$, we have: - Professionaloutdoormedia

Since $\cos 60^\circ = \frac12$, we have: - Professionaloutdoormedia

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 A train leaves Station A at 60 mph. Two hours later, a faster train leaves Station A on the same track at 90 mph. How long will it take the faster train to catch up?

📌 In 2 hours, first train travels: 60 × 2 = 120 miles

📌 Relative speed: 90 – 60 = 30 mph

📌 Time to catch up: 120 / 30 = 4 hours

📌 The sum of the squares of two consecutive positive integers is 145. What is the larger integer?

📌 Let integers be x and x+1

📌 Equation: x² + (x+1)² = 145 → x² + x² + 2x + 1 = 145 → 2x² + 2x + 1 = 145

📌 2x² + 2x – 144 = 0 → x² + x – 72 = 0

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