Пусть х км/ч - собственная скорость катера, тогда (х - 3) км/ч - скорость катера против течения реки, (х + 3) км/ч - скорость катера по течению реки. 7 - 2 = 5 ч - время движения. Уравнение:
36/(х-3) + 36/(х+3) = 5
36 · (х + 3) + 36 · (х - 3) = 5 · (х + 3) · (х - 3)
36х + 108 + 36х - 108 = 5 · (х² - 3²)
72х = 5х² - 45
5х² - 72х - 45 = 0
D = b² - 4ac = (-72)² - 4 · 5 · (-45) = 5184 + 900 = 6084
√D = √6084 = 78
х₁ = (72-78)/(2·5) = -6/10 (не подходит, так как < 0)
х₂ = (72+78)/(2·5) = 150/10 = 15
ответ: 15 км/ч - собственная скорость катера.
Проверка:
36 : (15 - 3) = 36 : 12 = 3 ч - время движения против течения
36 : (15 + 3) = 36 : 18 = 2 ч - время движения по течению
3 ч + 2 ч + 2 ч (остановка) = 7 ч - общее время на путь туда и обратно
Пошаговое объяснение:
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1)32+32=64 рубля Саша потратит на 2 пакета молока
2) 27*3=81 рублей Саша потратит на 3 пакета кефира
3) 64+81+27= 172 рублей потратил Саша.
4)200-172=28 рублей сдачи осталось у Саши
Саше не хватит купить еще один пакет молока, так как у него не хватит на него 4 рубля