Вопрос школьника по предмету Алгебра
Моторная лодка прошла по течению реки 20 км а против течения 30 км Найдите собственную скорость лодки если скорость течения реки равна 3 км ч На весь путь затрачено 6:40
Ответ учителя по предмету Алгебра
Пусть V собств = х км/ч
учтём, что 6:40 = 6ч 40мин = 6 40/60ч = 6 2/3 ч = 20/3 ч
S V t
по теч. 20км х +3 км/ч 20/(х +3)ч
пр. теч. 30 км х -3 км/ч 30/(х -3) ч
20/(х +3) + 30/(х -3) = 20/3
60(х -3) + 90(х +3) = 20(х² -9)
60х -180 +90х +270 = 20х² -180
20х² — 150х -270=0
2х² -15х -27 = 0
D = 441
x = (15+21)/4 = 9
х = (15 -21)/4 = -6/4(не подходит по условию задачи)
Ответ: V собств = 9 км/ч
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