Question

1107. Два слесаря получили задание. Для его выполнения первому слесарю понадобится на 7 ч больше, чем второму. После того как оба слесаря выполнили половину задания, работу пришлось заканчивать одному второму слесарю и поэтому задание было выполнено на 4,5ч позднее, чем если бы всю работу они выполнили вместе. За сколько часов мог бы выполнить задание каждый слесарь?

Answer 1

Объяснение:

Принимаем всю работу за единицу(1).

Пусть количество часов, за которое мог бы выполнить всю работу второй слесарь равна х час.                ⇒

Количество часов, за которое мог бы выполнить всю работу первый слесарь равна (х+7) час.

Тогда скорость выполнения всей работы вторым слесарем равна 1/х,

а скорость выполнения всей работы первым слесарем равна 1/(х+7).

$\frac{0,5}{\frac{1}{x+7}+\frac{1}{x} } +\frac{0,5}{\frac{1}{x} }-\frac{1}{\frac{1}{x+7}+\frac{1}{x} } =4,5\\ \frac{0,5*x*(x+7)}{x+x+7} +0,5x-\frac{x*(x+7)}{x+x+7} =4,5\\\frac{0,5*x^2+3,5x}{2x+7} +\frac{0,5x*(2x+7)}{2x+7} -\frac{x^2+7x}{2x+7} =4,5\\0,5x^2+3,5x+x^2+3,5x-x^2-7x=4,5*(2x+7x)\\0,5x^2=9x+31,5\\0,5x^2-9x-31,5=0\ |*2\\x^2-18x+63=0\\D=576\ \ \ \ \sqrt{D}=24\\x_1=-3\notin\ \ \ \ x_2=21\in.\\21+7=28.$

Ответ: всю работу первый слесарь мог бы выполнить за 28 часов.

            всю работу второй слесарь мог бы выполнить за 21 час.

Answer 2

Problem Analysis

We are given that two locksmiths have been assigned a task. The first locksmith will take 7 hours longer than the second locksmith to complete the task. After both locksmiths have completed half of the task, the second locksmith has to finish the remaining work alone. As a result, the task is completed 4.5 hours later than if both locksmiths had worked together. We need to determine how many hours each locksmith would take to complete the task individually.

Solution

Let's assume that the second locksmith takes x hours to complete the task. According to the given information, the first locksmith will take 7 hours longer, so the first locksmith will take (x + 7) hours to complete the task.

After both locksmiths have completed half of the task, the remaining work is completed by the second locksmith alone. This means that the second locksmith takes half the time to complete the remaining work compared to the time taken by both locksmiths together. Therefore, the second locksmith takes (4.5 / 2) = 2.25 hours to complete the remaining work.

To find the total time taken by both locksmiths together, we can add the time taken by the first locksmith to complete the task and the time taken by the second locksmith to complete the remaining work. This should be equal to the time taken when both locksmiths work together.

So, we can set up the following equation:

(x + 7) + 2.25 = x

Simplifying the equation:

x + 7 + 2.25 = x

9.25 = x - x

9.25 = 0

This equation is not possible to solve because it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The equation derived from the problem leads to a contradiction, indicating that the problem is not solvable.