Question

Помогите решить задачу!!!!!! Цех должен был изготовить 540 деталей.Фактически он выпускал в день на 3' детали больше плана и выполнил заказ на 9 дней раньше срока .За сколько дней был выполнен заказ? Пожалуйста очень важно!

Answer 1

Х дней должен был работать
х-9 работал
540/(х-9)-540/9=3
540х-540х+4860=3х²-27х
3х²-27х-4860=0
х²-9х-1620=0
х=(9+√(81+6480))/2 =(9+81)/2=45 дней
45-9=36 дней сделали зпказ

Answer 2

Problem Analysis

To solve this problem, we need to determine how many days it took for the workshop to complete the order of 540 parts. We are given that the workshop produced 3 more parts per day than planned and completed the order 9 days ahead of schedule.

Solution

Let's assume that the workshop produced x parts per day according to the plan. Since the workshop produced 3 more parts per day than planned, the actual production per day can be represented as (x + 3).

We know that the workshop completed the order 9 days ahead of schedule. Therefore, the number of days it took to complete the order can be represented as (x - 9).

According to the given information, the workshop produced 540 parts in total. We can set up the following equation to solve for x:

(x + 3) * (x - 9) = 540

Simplifying the equation:

x^2 - 6x - 567 = 0

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

Quadratic Equation Solution

Using the quadratic formula, we can find the value of x:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -6, and c = -567.

Calculating the discriminant:

D = b^2 - 4ac = (-6)^2 - 4(1)(-567) = 36 + 2268 = 2304

Since the discriminant is positive, we have two real solutions for x.

Calculating the solutions:

x = (-(-6) ± √(2304)) / (2 * 1) x = (6 ± 48) / 2

Simplifying:

x1 = (6 + 48) / 2 = 54 / 2 = 27 x2 = (6 - 48) / 2 = -42 / 2 = -21

Since the number of parts produced per day cannot be negative, we discard the negative solution.

Therefore, the workshop produced 27 parts per day according to the plan.

Calculation of Days to Complete the Order

Now that we know the number of parts produced per day according to the plan (27) and the number of additional parts produced per day (3), we can calculate the number of days it took to complete the order.

The actual production per day is (27 + 3) = 30 parts.

To calculate the number of days, we divide the total number of parts (540) by the actual production per day (30):

Number of days = 540 / 30 = 18

Therefore, the workshop completed the order in 18 days.

Answer

The workshop completed the order in 18 days.