1.
Средняя скорость - это ВЕСЬ путь поделить на ВСЁ время
5/3 * 120 = 200 км - первый участок пути
10/3 * 90 = 300 км - второй участок пути
200 + 300 = 500 км - весь путь
5/3 + 10/3 = 15/3 = 5 часов - всё время
500/5 = 100 км/ч - средняя скорость
2.
Пусть скорость лодки равна х км/ч, а скорость течения у км/ч
Тогда 49,2 км можно проплыть за 3 часа со скоростью (х+у) км/ч
Значит, справделиво уравнение: 3(х+у)=49,2
С другой стороны, эти же 49,2 км можно проплыть за 4 часа со скоростью (х-у) км/ч, отсюда уравнение: 4(х-у)=49,2
Получаем систему уравнений:
3(х+у)=49,2
4(х-у)=49,2
С первого уравнения выразим х:
3(х+у)=49,2
х+у=16,4
х=16,4-у
Подставим вместо икса во второе уравнение
4(х-у)=49,2
4(16,4-у-у)=49,2
4(16,4-2у)=49,2
16,4-2у=12,3
2у=4,1
у=2,05 км/ч - скорость течения
3. Допустим, расстояние между пунктами А и В равно S
Скорость плота - это скорость течения, значит, оно равно S/30 км/ч
Скорость движения катера - это скорость самого катера плюс скорость течения, значит, V + S/30 = S/3, отсюда V = S/3 - S/30 = 9S/30 = 3S/10
В обратную сторону течение будет тормозить катер, поэтому скорость его движения - это собственная скорость минус скорость течения:
V = 3S/10 - S/30 = 8S/30 = 4S/15
Найдём время, поделив весь путь S на скорость движения 4S/15:
S : 4S/15 = 15/4 часа = 3 часа 45 минут
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