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Консультация № 194925
10.03.2019, 16:08
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Пункты А и В расположены на одной реке так, что плот, плывущий из А в В со скоростью течения реки, проходит путь от А до В за 24 часа. Весь путь от А до В и обратно моторная лодка проходит не менее, чем за 10 часов. Если бы собственная скорость (т.е. скорость в стоячей воде) моторной лодки увеличилась на 40%, то путь от А до В и обратно занял бы у лодки не более 7 часов. Найти время, за которое моторная лодка проходит путь от А до В в случае, когда её собственная скорость не увеличена.
Пункты А и В расположены на одной реке так, что плот, плывущий из А в В со скоростью течения реки, проходит путь от А до В за 24 часа. Весь путь от А до В и обратно моторная лодка проходит не менее, чем за 10 часов. Если бы собственная скорость (т.е. скорость в стоячей воде) моторной лодки увеличилась на 40%, то путь от А до В и обратно занял бы у лодки не более 7 часов. Найти время, за которое моторная лодка проходит путь от А до В в случае, когда её собственная скорость не увеличена.
Обсуждение
12.03.2019, 11:31
общий
это ответ
Здравствуйте, Лилия!
Имеем
км -- расстояние между пунктами 
и 
км/ч -- скорость течения реки;
км/ч -- собственная скорость моторной лодки;
Обозначим отношение абсолютных величин собственной скорости моторной лодки к скорости течения как
Тогда система уравнения и неравенств примет следующий вид:
или 
или 
Решая неравенство (1), получим, что
или 
Решая неравенство (2), получим, что 
или 
или 
Поскольку должно быть 
постольку получим, что 
то есть 
Тогда
искомая величина равна
(ч.).
Имеем
км -- расстояние между пунктами и км/ч -- скорость течения реки; км/ч -- собственная скорость моторной лодки;Обозначим отношение абсолютных величин собственной скорости моторной лодки к скорости течения как
Тогда система уравнения и неравенств примет следующий вид: или или Решая неравенство (1), получим, что
или Решая неравенство (2), получим, что или или Поскольку должно быть постольку получим, что то есть Тогдаискомая величина равна
(ч.).
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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