Question

Ученик изготавливает в час на 8 деталей меньше, чем мастер. ученик работал 7 часов, а мастер 3 часа. сколько деталей в час изготавливает ученик, если они изготовили одинаковое количество деталей?

Answer 1

Х-8*7=х*3
3х=7х-56
3х-7х=-56
4х=56
х=14

Answer 2

Problem Analysis

We are given that a student produces 8 fewer parts per hour than a master. The student worked for 7 hours, and the master worked for 3 hours. We need to determine how many parts per hour the student produces if they both produced the same number of parts.

Solution

Let's assume that the master produces x parts per hour. According to the given information, the student produces 8 fewer parts per hour than the master. Therefore, the student produces (x - 8) parts per hour.

To find the total number of parts produced by the student and the master, we can multiply their respective production rates by the number of hours they worked. The total number of parts produced by the student is (x - 8) * 7, and the total number of parts produced by the master is x * 3.

Since they both produced the same number of parts, we can set up the following equation:

(x - 8) * 7 = x * 3

Let's solve this equation to find the value of x, which represents the number of parts per hour produced by the master.

Solving the Equation

Expanding the equation, we get:

7x - 56 = 3x

Combining like terms, we have:

7x - 3x = 56

Simplifying, we get:

4x = 56

Dividing both sides by 4, we find:

x = 14

Therefore, the master produces 14 parts per hour.

To find the number of parts per hour produced by the student, we substitute the value of x into the expression (x - 8):

14 - 8 = 6

Therefore, the student produces 6 parts per hour.

Answer

The student produces 6 parts per hour if they both produced the same number of parts.

Verification

Let's verify our answer by checking if the total number of parts produced by the student and the master is the same.

The total number of parts produced by the student is (6 parts/hour) * (7 hours) = 42 parts.

The total number of parts produced by the master is (14 parts/hour) * (3 hours) = 42 parts.

Since both the student and the master produced the same number of parts (42 parts), our answer is verified.

Conclusion

The student produces 6 parts per hour if they both produced the same number of parts.