Question

Двоє робітників виготовили 123 деталі. Перший робітник працював 7 год, а другий — 10 год. Скільки деталей виготовляв за 1 год кожний робітник, якщо перший за 4 год зробив на 6 деталей більше, ніж другий за 5 год?

Answer 1

Пусть 1-й работник за час делал Х дет., а 2-й - У дет.,  тогда 1-й за час сделает 4Х дет., за 7 часов - 7Х дет., а 2-й - за 5 часов 5У дет., а за 10 часов: 10У дет. Составим систему уравнений:

4Х-5У=6

7Х+10У=123     Решим эту систему уравнений методом сложения, для этого все части 1-го ур-нения умножим на (-7), а все части 2-го ур-нения умножим на 4, получим:  -28Х+35У= -42

28Х+40У=492

Складываем оба ур-нения, получаем:

75У=450   У=6   Подставляем это значение в изначальное ур-нение: 4Х-5*6=6,  4Х-30=6, 4Х=36, Х=9.

Ответ: 1-й рабочий за час изготовлял 9 деталей, а второй - 6 деталей.

 

Answer 2

Calculation of Production Rate for Each Worker

To determine the number of parts produced per hour by each worker, we need to calculate the production rate for each worker based on the given information.

Let's break down the information provided:

- Two workers produced a total of 123 parts. - The first worker worked for 7 hours. - The second worker worked for 10 hours. - The first worker produced 6 more parts in 4 hours than the second worker produced in 5 hours.

To find the production rate for each worker, we can use the following steps:

1. Calculate the production rate for the first worker: - Let's assume the production rate for the first worker is x parts per hour. - In 7 hours, the first worker produced a total of 7x parts.

2. Calculate the production rate for the second worker: - Let's assume the production rate for the second worker is y parts per hour. - In 10 hours, the second worker produced a total of 10y parts.

3. Use the information about the additional parts produced by the first worker: - In 4 hours, the first worker produced 6 more parts than the second worker produced in 5 hours. - This can be expressed as: 7x - 4x = (10y - 5y) + 6.

Now, let's solve the equation to find the production rates for each worker.

Solving the Equation

7x - 4x = (10y - 5y) + 6

Simplifying the equation:

3x = 5y + 6

To find the values of x and y, we need another equation. We can use the total number of parts produced to create a second equation.

Using the Total Number of Parts Produced

The total number of parts produced by both workers is 123. We can express this as:

7x + 10y = 123

Now we have a system of equations:

3x = 5y + 6 7x + 10y = 123

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

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

Multiply the first equation by 2 to make the coefficients of x in both equations equal:

6x = 10y + 12

Now we have:

6x = 10y + 12 7x + 10y = 123

Subtract the first equation from the second equation:

(7x + 10y) - (6x = 10y + 12)

x = 111 - 12 x = 99

Substitute the value of x back into the first equation to find y:

3(99) = 5y + 6 297 = 5y + 6 5y = 297 - 6 5y = 291 y = 291/5 y = 58.2

Results

After solving the system of equations, we find that the production rate for the first worker is approximately 99 parts per hour, and the production rate for the second worker is approximately 58.2 parts per hour.

Therefore, the first worker produced approximately 99 parts per hour, and the second worker produced approximately 58.2 parts per hour.

Please note that the production rates are approximate values based on the calculations.