Question

70 баллов Два маляра, работая вместе, могут покрасить фасад дома за 12 часов. За сколько часов может выполнить эту работу каждый из них, работая самостоятельно, если первому для этого нужно на 18 ч меньше, чем второму ? Развернутое решение, пожалуйста

Answer 1

Ответ: 18 часов, 36 часов

Объяснение:

1- вся работа.

пусть первому надо х час., чтобы выполнить работу самостоятельно. тогда второму необходимо (х+18) час. , производительность первого

1/х, второго - 1/(х+18);

составим и решим уравнение.

1/х+ 1/(х+18)=1/12;

х≠0; х≠-18;

12*(х+18+х)=х²+18х;

24х+12*18=х²+18х;

х²-6х-12*18=0;

х=3±√(9+12*18)=3±15; х=18; х=-12 - не подходит по смыслу задачи.

Первый маляр выполнит работу, работая самостоятельно за 18 часов, второй за 18+18=36/ час/

Answer 2

Problem Analysis

We are given that two painters can paint the facade of a house together in 12 hours. We need to find out how long it would take each painter to complete the job individually, given that the first painter takes 18 hours less than the second painter.

Solution

Let's assume that the second painter takes x hours to complete the job individually. According to the given information, the first painter takes 18 hours less than the second painter, so the first painter would take (x - 18) hours to complete the job individually.

To find the individual rates of each painter, we can use the formula:

Rate = Work / Time

The rate of the first painter is the work done by the first painter divided by the time taken by the first painter. Similarly, the rate of the second painter is the work done by the second painter divided by the time taken by the second painter.

Since both painters are working on the same job, the work done by each painter is the same. Therefore, we can equate the rates of the two painters:

Rate of the first painter = Rate of the second painter

Using the formula for rate, we can write the equation as:

Work / (x - 18) = Work / x

Simplifying the equation, we get:

x = (x - 18) * 12

Now, let's solve this equation to find the value of x.

Calculation

Expanding the equation:

x = 12x - 216

Bringing like terms together:

x - 12x = -216

Simplifying:

-11x = -216

Dividing both sides by -11:

x = 216 / 11

Calculating the value of x:

x ≈ 19.64

Therefore, the second painter would take approximately 19.64 hours to complete the job individually.

To find the time taken by the first painter, we can substitute the value of x into the equation:

Time taken by the first painter = x - 18

Time taken by the first painter ≈ 19.64 - 18 ≈ 1.64

Therefore, the first painter would take approximately 1.64 hours to complete the job individually.

Answer

The second painter would take approximately 19.64 hours to complete the job individually, while the first painter would take approximately 1.64 hours to complete the job individually.

Note: The above solution assumes that the rates of work for each painter remain constant when working individually.