Question

Одному маляру нужно на 4 ч больше,чтобы покрасить комнату, чем другому. Если первый маляр проработает 3 ч, а потом его сменит второй, то последни докрасит эту комнату за 6 ч. За сколько часов может покрасить всю комнату второй маляр?

Answer 1

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Answer 2

Обозначим время, которое нужно затратить второму маляру x, тогда время первого маляра х+4. Скорость работы (или производительность) первого тогда выйдет $\frac{1}{x+4}$ а второго $\frac{1}{x}$.
Записать условие их совместной работы можно так
$1= \frac{3}{x+4}+ \frac{6}{x}$
Мы сложили работу первого маляра за 3 часа и второго маляра за 6.
Упрощаем.
$1= \frac{3x+6+24}{x(x+4)} \\ 9x+24=x^2+4x \\ x^2-5x-24=0 \\ D=25+4*24=121 \\ x_1=8, x_2<0$

Второй корень ложный, так как время не может быть отрицательным. Значит х=8, что и требовалось найти.
Ответ: 8ч

Answer 3

Problem Analysis

We have two painters, and one of them takes 4 hours more than the other to paint a room. The first painter works for 3 hours, and then the second painter takes over and finishes painting the room in 6 hours. We need to determine how long it would take the second painter to paint the entire room.

Solution

Let's assume that the first painter takes x hours to paint the room. According to the problem, the second painter takes 4 hours less than the first painter, so the second painter takes (x - 4) hours to paint the room.

We are given that the first painter works for 3 hours and then the second painter takes over and finishes painting the room in 6 hours. From this information, we can set up the following equation:

3 hours of work by the first painter + 6 hours of work by the second painter = total time to paint the room

Mathematically, this can be represented as:

3 + (x - 4) = x

Simplifying the equation:

3 + x - 4 = x

x - x = 4 - 3

0 = 1

The equation is inconsistent, which means there is no solution that satisfies the given conditions. Therefore, it is not possible to determine how long it would take the second painter to paint the entire room based on the information provided.

Note: The given problem may have some inconsistencies or errors. If you have any additional information or clarification, please provide it so that we can provide a more accurate solution.