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Home » Sea x la cantidad de agua agregada. Entonces, (90 + x) / 490 = 5 / 7. - Dachbleche24

Sea x la cantidad de agua agregada. Entonces, (90 + x) / 490 = 5 / 7. - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 #### 10 et 12

📌 Une voiture parcourt 240 km à une vitesse constante. Si elle augmente sa vitesse de 10 km/h, elle parcourt la même distance en 1 heure de moins. Quelle était la vitesse initiale de la voiture ?

📌 Soit la vitesse initiale \( v \) km/h.

📌 Le temps nécessaire à la vitesse initiale est \( \frac{240}{v} \) heures.

📌 À \( v + 10 \) km/h, le temps est \( \frac{240}{v + 10} \) heures.

📌 L’équation est \( \frac{240}{v} - 1 = \frac{240}{v + 10} \).

📌 En multipliant et en simplifiant, on obtient \( 240(v + 10) - v(v + 10) = 240v \), ce qui donne \( 2400 - v^2 - 10v = 0 \) ou \( v^2 + 10v - 2400 = 0 \).

📌 En résolvant l’équation quadratique, \( (v + 60)(v - 50) = 0 \), donc \( v = 50 \) km/h.

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