Question

Одному рабочему надо было изготовить 90 деталей , а другому 60 деталей. Первый рабочий ежедневно изготавливал 4 деталей, а второй 5 деталей. Через сколько дней первому рабочему останется изготовить в 2 раза больше деталей, чем второму, если они начали работать в один день?

Answer 1

90-4х=2*(60-5х)
90-4х=120-10х
-10х+4х=120-90
6х=30
х=60:3
х=5
ответ:5

Answer 2

Problem Analysis

We have two workers who need to manufacture a certain number of parts. The first worker needs to make 90 parts, while the second worker needs to make 60 parts. The first worker can produce 4 parts per day, while the second worker can produce 5 parts per day. We need to determine how many days it will take for the first worker to have twice as many parts left to make compared to the second worker.

Solution

To solve this problem, we can set up an equation to represent the number of parts each worker has left to make at a given time. Let's assume that both workers start working on the same day.

Let's denote: - x as the number of days it takes for the first worker to have twice as many parts left to make compared to the second worker. - P1 as the number of parts the first worker has left to make after x days. - P2 as the number of parts the second worker has left to make after x days.

Based on the given information, we can set up the following equations:

Equation 1: P1 = 90 - 4x (The first worker starts with 90 parts and produces 4 parts per day) Equation 2: P2 = 60 - 5x (The second worker starts with 60 parts and produces 5 parts per day)

We want to find the value of x when P1 is twice as large as P2. Mathematically, this can be represented as:

Equation 3: P1 = 2P2

Substituting Equations 1 and 2 into Equation 3, we get:

90 - 4x = 2(60 - 5x)

Simplifying the equation:

90 - 4x = 120 - 10x

Adding 10x to both sides:

10x - 4x = 120 - 90

Simplifying further:

6x = 30

Dividing both sides by 6:

x = 5

Therefore, it will take the first worker 5 days to have twice as many parts left to make compared to the second worker.

Answer

The first worker will have twice as many parts left to make compared to the second worker after 5 days of work.