Предмет: Алгебра, автор: energiatela

Майстер і учень, працюючи разом, можуть виконати замовлення за 20 год. За скільки годин учень виконає це саме замовлення самостійно, якщо йому на це потрібно на 75 год більше, ніж майстру?
даю 15 б

Ответы

Автор ответа: Пеппер

Ответ:

85 годин.

Объяснение:

Нехай учень виконає замовлення за х годин, тоді майстер за х-75 годин.

За 1 годину учень виконає 1/х частину замовлення.

За 1 годину майстер виконає 1/(х-75) частину замовлення.

Разом за 1 годину вони виконають 1/20 частину замовлення.

1/х + 1/(х-75) = 1/20

20х-1500+20х-х²+75х=0

х²-115х+1500=0

За теоремою Вієта х=5 (не підходить) х=85

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