Два мастера, работая вместе, могут выстелить стену за 12 дней. Если первый масте...

July 2022 1 31 Report

Два мастера, работая вместе, могут выстелить стену за 12 дней. Если первый мастер проработает 2 дня, а второй - 3 дня, они сделают только 20% всей работы. За сколько дней каждый из мастеров сделает всю работу?

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sangers1959

Verified answer

Объяснение:

Принимаем всю работу за единицу (1).

Пусть скорость работы первого мастера равна х, а скорость работы второго мастера равна у. ⇒

$\left \{ {{x+y=\frac{1}{12} \ |*12} \atop {2*x+3*y=\frac{1*20\%}{100\%} }} \right. \ \ \ \ \left \{ {{12x+12y=1} \atop {2x+3y=0,2\ |*4}} \right. \ \ \ \ \left \{ {{12x+12y=1} \atop {8x+12y=0,8}} \right. .$

Вычитаем из первого уравнения второе:

$4x=0,2=\frac{1}{5} \ |:4\\x=\frac{1}{20}.\\2*\frac{1}{20}+3y=0,2\\\frac{1}{10} +3y=\frac{2}{10}\\3y=\frac{1}{10} \ |:3\\y=\frac{1}{30}. \ \ \ \ \Rightarrow$

Количество дней, за которые первый мастер сделает всю работу:

$\frac{1}{\frac{1}{20} } =20.$

Количество дней, за которые второй мастер сделает всю работу:

$\frac{1}{\frac{1}{30} } =30.$

Ответ: 20 дней, 30 дней.

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