Question

Два станка-автомата за 1 час общей работы изготавливают 250 деталей. Первый станок за 4 часа и второй за два часа вместе изготавливают 740 деталей . Сколько деталей изготавливает каждый станок за 1 час?

Answer 1

Пусть первый станок это A а второй B
A+B = 250 деталей
4часа * A + 2часа * B = 740
4A+2B=740

Выражаем A через B
A = 250-B
Подставляем А во второе уравнение

4(250-B)+2B=740
1000-4B+2B = 740
1000-740 = 4B-2B
260 = 2B
B = 130 деталей за один час
тогда станок A = 250-130=120 Деталей в час

Проверяем их работу во втором случае 4 часа
4A+2B=740
4*120+2*130=480+260=740 деталей

Ответ верный.

Answer 2

Calculation of Production Rate for Each Machine

To determine the number of parts each machine produces per hour, we can set up a system of equations based on the given information.

Let's assume that the first machine produces x parts per hour, and the second machine produces y parts per hour.

From the first statement, we know that two machines working together can produce 250 parts in 1 hour. This can be expressed as:

x + y = 250 From the second statement, we know that the first machine can produce 740 parts in 4 hours, and the second machine can produce 740 parts in 2 hours when they work together. This can be expressed as:

4x + 2y = 740

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

Multiplying the first equation by 2, we get:

2x + 2y = 500

Subtracting the second equation from the modified first equation, we get:

(2x + 2y) - (4x + 2y) = 500 - 740

Simplifying, we have:

-2x = -240

Dividing both sides by -2, we find:

x = 120

Substituting the value of x into the first equation, we can solve for y:

120 + y = 250

Simplifying, we have:

y = 130

Therefore, the first machine produces 120 parts per hour, and the second machine produces 130 parts per hour.