Question

За 6 ч работы ученик сделал столько же деталей, сколько мастер за 4 ч. Известно, что мастер изготовлял в час на 5 деталей больше, чем ученик. Сколько деталей в час изготовлял ученик?

Answer 1

Пусть х дет. изготавливает за 1 час ученик.

Тогда: (х+5) дет. изготавливает мастер за 1 час.

Зная, что за кол-во деталей, изготовленное учеником за 6 часов и мастером за 4 часа одинаково, составим и решим уравнение.

6*х=4*(х+5)

6х=4х+20

6х-4х=20

2х=20

х=20/2

х=10

Ответ: 10 деталей изготавливает ученик за час.

Answer 2

Problem Analysis

We are given that a student made the same number of parts in 6 hours as a master made in 4 hours. It is also known that the master made 5 more parts per hour than the student. We need to determine how many parts the student made per hour.

Solution

Let's assume that the student made x parts per hour. Since the master made 5 more parts per hour than the student, the master made (x + 5) parts per hour.

According to the given information, the student made the same number of parts in 6 hours as the master made in 4 hours. We can set up the following equation to represent this:

6x = 4(x + 5)

Now, let's solve this equation to find the value of x, which represents the number of parts the student made per hour.

Calculation

6x = 4(x + 5)

Expanding the equation: 6x = 4x + 20

Subtracting 4x from both sides: 2x = 20

Dividing both sides by 2: x = 10

Answer

The student made 10 parts per hour.

Explanation

Based on the given information, the student made the same number of parts in 6 hours as the master made in 4 hours. Since the master made 5 more parts per hour than the student, we can conclude that the student made 10 parts per hour. This satisfies the condition that the student made the same number of parts in 6 hours as the master made in 4 hours.

Verification

Let's verify our answer by substituting the value of x into the equation:

6x = 4(x + 5) 6(10) = 4(10 + 5) 60 = 4(15) 60 = 60

The equation is balanced, which confirms that our answer is correct.