Question

Две бригады, работая вместе могут выполнить задание за 8 дней. Первая бригада, работая одна могла бы выполнить задание на 12 дней быстрее, чем вторая бригада Производительность = P Работа = A Время = t p1 = x p2 = y

Answer 1

Пусть х - время за которое работу выполнит 1я бригада; у - 2я, тогда А/х скорость работы 1ой бригады (работы в день), А/у - 2ой бригады.
А/8 - это производительность двух бригад вместе: (А/х+А/у)=А/8;
у=х+12, потому что первая бригада сможет сделать эту работу на 12 дней раньше.
значит (А/х+А/(х+12))=А/8;
разделим все на А,
(1/х+1/(х+12))=1/8;
((х+12+х)/х(х+12))-1/8=0;
((2х+12)/х(х+12))-1/8=0; умножим на 8х(х+12);
8(2х+12)-(х^2+12х)=0;
16х+96-х^2-12х=0;
х^2-4х-96=0;
представим -4х как -12х+8х;
х^2+8х-12х-96=0;
х(х+8)-12(х+8)=0;
(х+8)(х-12)=0;
х=-8 или х=12;
отрицательное значение не имеет смысла, значит первая бригада может выполнить работу за 12 дней;
2я бригада за 12+12=24 дня.
Ответ: 1я бригада сделает работу за 12 дней, 2я - за 24 дня.

Answer 2

Task Analysis

We are given the following information: - Two brigades working together can complete a task in 8 days. - The first brigade working alone can complete the task 12 days faster than the second brigade.

We need to determine the individual productivity of each brigade and the time it would take for each brigade to complete the task alone.

Solution

Let's assume the productivity of the first brigade is P1 and the productivity of the second brigade is P2. We are also given that the time taken by the first brigade alone is 12 days less than the time taken by the second brigade alone.

Using the formula Work = Productivity × Time, we can set up the following equations:

Equation 1: (P1 + P2) × 8 = 1 (Two brigades working together complete the task in 8 days)

Equation 2: P1 × (t + 12) = 1 (First brigade alone completes the task t days faster than the second brigade alone)

Simplifying Equation 1, we get:

(P1 + P2) × 8 = 1

Simplifying Equation 2, we get:

P1 × t + 12P1 = 1

Now, let's solve these equations to find the values of P1, P2, and t.

Calculation

To solve the equations, we can use substitution or elimination method. Let's use the elimination method:

Multiplying Equation 2 by 8, we get:

8P1 × t + 96P1 = 8

Subtracting Equation 1 from the above equation, we get:

8P1 × t + 96P1 - 8P1 - 8P2 = 8 - 1

Simplifying further, we get:

8P1 × t + 88P1 - 8P2 = 7

Now, let's substitute the value of 8P1 × t from Equation 2 into the above equation:

(1 - 12P1) + 88P1 - 8P2 = 7

Simplifying further, we get:

-11P1 - 8P2 = 6

Now, we have two equations:

Equation 3: P1 + P2 = 1/8

Equation 4: -11P1 - 8P2 = 6

Now, we can solve these equations to find the values of P1 and P2.

Solution

Solving Equations 3 and 4, we find:

P1 = 1/40

P2 = 7/40

Now, let's find the time taken by each brigade to complete the task alone.

Using Equation 2, we can substitute the value of P1 and solve for t:

(1/40) × (t + 12) = 1

Simplifying, we get:

t + 12 = 40

t = 28

Therefore, the first brigade would take 28 days to complete the task alone, and the second brigade would take 40 days to complete the task alone.

Answer

The first brigade, working alone, would take 28 days to complete the task, while the second brigade, working alone, would take 40 days to complete the task.