Question

С помощью систем уравнения решите задачу двое рабочих работая одновременно могут выполнить работу за 60 часов однако после 12 часов совместной работы первый рабочий прекратил ее выполнять и для завершения работы второму потребовалось 80 часов за какое время каждый рабочий мог бы выполнить работу делая ее отдельно ( помогите очень нужно пожалуйста)

Answer 1

Всё подробно написала  в решении.

Answer 2

Problem Analysis

We are given that two workers can complete a job together in 60 hours. However, after working together for 12 hours, the first worker stops, and it takes the second worker an additional 80 hours to complete the job alone. We need to determine how long each worker would take to complete the job individually.

Let's assume that the first worker takes x hours to complete the job alone, and the second worker takes y hours to complete the job alone.

Solution

To solve this problem, we can set up a system of equations based on the given information.

Equation 1: (1/x + 1/y) * 12 = 1 (This equation represents the work done by both workers in the first 12 hours, which is equal to the work done by one worker in 12 hours.)

Equation 2: 1/x * (12 + 80) = 1 (This equation represents the work done by the second worker in the remaining 80 hours to complete the job.)

Now, let's solve this system of equations to find the values of x and y.

Solving the System of Equations

From Equation 1, we can simplify it to:

(1/x + 1/y) * 12 = 1

Simplifying further, we get:

12/y + 12/x = 1

Multiplying both sides of the equation by xy, we get:

12x + 12y = xy

From Equation 2, we can simplify it to:

1/x * (12 + 80) = 1

Simplifying further, we get:

(12 + 80)/x = 1

Multiplying both sides of the equation by x, we get:

12 + 80 = x

Simplifying, we find:

x = 92

Now, we can substitute the value of x into Equation 1 to find y:

12/y + 12/92 = 1

Multiplying both sides of the equation by 92y, we get:

12*92 + 12y = 92y

Simplifying, we find:

12*92 = 80y

Simplifying further, we get:

y = 11

Therefore, the first worker would take 92 hours to complete the job alone, and the second worker would take 11 hours to complete the job alone.

Answer

Each worker would take the following amount of time to complete the job individually: - The first worker would take 92 hours. - The second worker would take 11 hours.