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Home » But we need integer — no solution? But problem asks for it. - DNSFLEX

But we need integer — no solution? But problem asks for it. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A car travels at a constant speed. It takes 3 hours to go from City A to City B, and on the return trip, it takes 2 hours. If the total round-trip distance is 500 km, what is the average speed for the entire journey?

📌 Total distance = 500 km (500 back and forth).

📌 Total time = 3 + 2 = 5 hours.

📌 Average speed = \( \frac{500}{5} = 100 \) km/h.

📌 Solve for \( x \): \( 3^{2x+1} = 81 \cdot 3^{x-1} \).

📌 Express 81 as \( 3^4 \), so equation becomes:

📌 \( 3^{2x+1} = 3^4 \cdot 3^{x-1} = 3^{4 + x - 1} = 3^{x+3} \).

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