Question

Два комбайна работая совместно могут выполнить задание за 6 ч. первый комбайн, работая один, может выполнить это задание на 5 ч скорее, чем второй комбайн. За сколько времени может выполнить задание первый комбайн, работая один? (только условие в форме таблицы)​

Answer 1

Task Analysis

We are given the following information: - Two combines working together can complete a task in 6 hours. - The first combine working alone can complete the task 5 hours faster than the second combine.

We need to determine how long it would take for the first combine to complete the task working alone.

Solution

Let's assume that the second combine takes x hours to complete the task working alone.

According to the given information, the first combine can complete the task 5 hours faster than the second combine. Therefore, the first combine would take (x - 5) hours to complete the task working alone.

When the two combines work together, they can complete the task in 6 hours.

To find the combined work rate of the two combines, we can use the formula:

1 / (x - 5) + 1 / x = 1 / 6

Simplifying this equation will give us the value of x, which represents the number of hours it takes for the second combine to complete the task working alone.

Let's solve this equation:

1 / (x - 5) + 1 / x = 1 / 6

Multiplying both sides of the equation by 6x(x - 5) to eliminate the denominators:

6x + 6(x - 5) = x(x - 5)

Simplifying further:

6x + 6x - 30 = x^2 - 5x

Combining like terms:

12x - 30 = x^2 - 5x

Rearranging the equation:

x^2 - 17x + 30 = 0

Now we can solve this quadratic equation to find the value of x.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -17, and c = 30.

Substituting the values into the quadratic formula:

x = (-(-17) ± √((-17)^2 - 4(1)(30))) / (2(1))

Simplifying:

x = (17 ± √(289 - 120)) / 2

x = (17 ± √169) / 2

x = (17 ± 13) / 2

We have two possible solutions:

1. x = (17 + 13) / 2 = 30 / 2 = 15 2. x = (17 - 13) / 2 = 4 / 2 = 2

Since the second combine cannot complete the task in 2 hours (as it would be faster than the first combine), the only valid solution is x = 15.

Therefore, the second combine takes 15 hours to complete the task working alone, and the first combine takes 15 - 5 = 10 hours to complete the task working alone.

Answer

The first combine, working alone, can complete the task in 10 hours.