Question

На новой модели станка изготавливают на 15 деталей в час больше, и таким образом, за 12 дней изготавливают на 100 деталей больше, чем раньше за 16 дней. Сколько деталей в день изготавливает старый станок? Решите задачу с помощью уравнения.

Answer 1

Х дет в час на старом станке, тогда (х+15)дет в час на новом станке, 16х всего деталей на старом станке , 12(х+15) всего деталей на новом станке, составляем формулу 12(х+15)-100=16х,12х+180-100=16х,12х-16х=-180+100,-4х=-80,х=20 деталей на старом станке

Answer 2

Problem Analysis

We are given that a new model of a machine produces 15 more parts per hour than the old model. Additionally, the new model produces 100 more parts in 12 days compared to the old model in 16 days. We need to determine how many parts the old machine produces per day.

Solution

Let's assume that the old machine produces x parts per hour. Therefore, the new machine produces x + 15 parts per hour.

To find the number of parts produced by the old machine in 16 days, we can use the formula:

Number of parts = (Number of hours per day) * (Number of days) * (Number of parts per hour)

For the old machine, the number of parts produced in 16 days is:

Number of parts produced by old machine = 24 * 16 * x

For the new machine, the number of parts produced in 12 days is:

Number of parts produced by new machine = 24 * 12 * (x + 15)

According to the problem, the new machine produces 100 more parts than the old machine in 12 days. Therefore, we can set up the equation:

24 * 12 * (x + 15) = 24 * 16 * x + 100

Simplifying the equation:

288x + 4320 = 384x + 100

Subtracting 384x from both sides:

288x - 384x + 4320 = 100

Combining like terms:

-96x + 4320 = 100

Subtracting 4320 from both sides:

-96x = -4220

Dividing both sides by -96:

x = 44.1667

Therefore, the old machine produces approximately 44.1667 parts per hour.

To find the number of parts produced by the old machine per day, we can divide the number of parts produced per hour by 24:

Number of parts produced by old machine per day = 44.1667 / 24

Simplifying:

Number of parts produced by old machine per day ≈ 1.8403

Therefore, the old machine produces approximately 1.8403 parts per day.

Answer

The old machine produces approximately 1.8403 parts per day.