Question

Продуктивність двох верстатів з програмним управлінням однакова.Один з них працював 7 годин,а інший--3 години.Перший верстат виробив на 140деталей більше,ніж другий.Яка продуктианість кожного верстата?

Answer 1

7 ч-3 ч=4 ч (за 4 часа первый произвел 140 деталей)
140 дет:4 ч=35 дет/ч (производительность станков)
35 дет/ч*7 ч=245 дет (первый)
35 дет/ч*3 ч=105 дет (второй)
Ответ: первый станок произвел 245 деталей, второй - 105 деталей

Проверка
245-105=140 (что соответствует условию)

Answer 2

Calculating the Productivity of Each Machine

To calculate the productivity of each machine, we can use the information provided about the number of hours each machine worked and the difference in the number of parts produced.

Let's denote: - Machine 1's productivity as P1 - Machine 2's productivity as P2 - The number of hours Machine 1 worked as H1 (7 hours) - The number of hours Machine 2 worked as H2 (3 hours) - The difference in the number of parts produced by the two machines as D (140 parts)

We can use the following formula to calculate the productivity of each machine: Productivity = (Number of parts produced) / (Number of hours worked)

Calculating the Productivity of Machine 1

Using the given information: - Machine 1 worked for 7 hours and produced 140 more parts than Machine 2.

We can calculate the productivity of Machine 1 as follows: P1 = (Number of parts produced by Machine 1) / (Number of hours worked by Machine 1) P1 = (P2 + 140) / 7 [[1]]

Calculating the Productivity of Machine 2

Using the given information: - Machine 2 worked for 3 hours.

We can calculate the productivity of Machine 2 as follows: P2 = (Number of parts produced by Machine 2) / (Number of hours worked by Machine 2) P2 = (P2) / 3 [[1]]

Solving for the Productivity of Each Machine

To solve for the productivity of each machine, we can use the relationship between the productivities of the two machines.

Substituting the expression for P2 from the equation for Machine 2's productivity into the equation for Machine 1's productivity, we get: (P2 + 140) / 7 = P2 / 3

Solving for P2: 3(P2 + 140) = 7P2 3P2 + 420 = 7P2 420 = 4P2 P2 = 105

Now that we have found the productivity of Machine 2, we can calculate the productivity of Machine 1 using the equation: P1 = (P2 + 140) / 7 P1 = (105 + 140) / 7 P1 = 245 / 7 P1 = 35

Conclusion

The productivity of Machine 1 is 35 parts per hour, and the productivity of Machine 2 is 105 parts per hour.