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1136. A boat traveled 50 km downstream and 45 km upstream, taking 10 hours to complete the journey. Find the boat's own speed if the river's current is 2,5 km/h. Write the boat's own velosity as x, create a table for the problem, and then write and solve the equation. Vвл = x км/год. Vтеч = 2,5 км/год. Розв'язання 50/(x+2,5) + 45/(x-2,5) = 10; 50^(\x-2,5)/(x+2,5) + 45^(\x+2,5)/(x-2,5) – 10^(\x^2-6,25) = 0; (50x-125+45x+112,5-〖10x〗^2+62,5)/((x+2,5)(x-2,5)) = 0, (• (x + 2,5)(x – 2,5)); –10x² + 95x + 50 = 0, (: (–5)); 2x² – 19x – 10 = 0; D = (–19)2 – 4 • 2 • (–10) = 361 + 80 = 441 = 21²; x1 = (19-21)/4 = (-2)/4 = –0,5 – не задовольняє умову; x2 = (19+21)/4 = 40/4 = 10. Vвл = 10 км/год. Відповідь: 10 км/год.