Question

Рабочему и ученику нужно было изготовить 80 деталей. После того, как ученик проработал 3 ч, к выполнению задания подключился рабочий, и они вместе закончили работу за 2 ч. Сколько деталей делает рабочий за один час, если рабочий за 4 ч делает столько же, сколько ученик за 10 ч?

Answer 1

х - производительность рабочего в часу - производительность ученика в час3х=4у х = 4у/33у + 2у + 2 * (4у/3)=699у + 6у + 8у = 20723у=207у = 9 - количество деталей изготовляемых учеником в 1 час, его производительностьх = 4*9/3=12 - количество деталей изготовляемых рабочим в 1 час, его производительность

Answer 2

Problem Analysis

To solve this problem, we need to determine how many parts the worker produces per hour. We are given the following information: - The worker completes the task in 4 hours, which is the same amount of time the student takes to complete the task in 10 hours. - After the student works for 3 hours, the worker joins and together they complete the task in 2 hours.

Let's denote the number of parts the worker produces per hour as W and the number of parts the student produces per hour as S.

Solution

To find the value of W, we can set up the following equation based on the given information:

(3 hours * S) + (2 hours * (S + W)) = 80 parts

Simplifying the equation, we get:

3S + 2(S + W) = 80

Simplifying further, we get:

3S + 2S + 2W = 80

Combining like terms, we get:

5S + 2W = 80

Now, let's use the additional information provided to solve for W.

We know that the worker completes the task in 4 hours, which is the same amount of time the student takes to complete the task in 10 hours. This gives us the equation:

4W = 10S

Simplifying, we get:

2W = 5S

Now, we have a system of equations:

5S + 2W = 80 2W = 5S

We can solve this system of equations to find the values of S and W.

Solution Steps

1. Substitute the value of 5S from the second equation into the first equation:

5S + 2(2W) = 80

Simplifying, we get:

5S + 4W = 80

2. Substitute the value of 10S from the second equation into the first equation:

5(2W) + 4W = 80

Simplifying, we get:

10W + 4W = 80

Combining like terms, we get:

14W = 80

3. Solve for W:

W = 80 / 14

Simplifying, we get:

W ≈ 5.71

Therefore, the worker produces approximately 5.71 parts per hour.

Answer

The worker produces approximately 5.71 parts per hour.

Note: The actual value may vary depending on the rounding method used.