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

Answer 1

Составляем систему уравнений.

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.

1. The first equation represents the work done by both workers together: - In 12 hours, they complete 12/60 of the job. - In x hours, the first worker completes x/x of the job (the entire job). - In y hours, the second worker completes y/y of the job (the entire job). - Therefore, the equation is: 12/60 + x/x + y/y = 1.

2. The second equation represents the work done by the second worker alone: - In 80 hours, the second worker completes 80/60 of the job. - In y hours, the second worker completes y/y of the job (the entire job). - Therefore, the equation is: 80/60 + y/y = 1.

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

Solution Steps

1. Simplify the first equation: - 12/60 + x/x + y/y = 1 - 1/5 + 1 + 1 = 1 - 1/5 + 1 + 1 = 1 - 1/5 + 5/5 + 5/5 = 1 - 11/5 = 1

2. Simplify the second equation: - 80/60 + y/y = 1 - 4/3 + 1 = 1 - 4/3 + 3/3 = 1 - 7/3 = 1

3. Solve for x: - From the first equation, we have 11/5 = 1. - Multiplying both sides by 5, we get 11 = 5. - This is not possible, so there is no solution for x.

4. Solve for y: - From the second equation, we have 7/3 = 1. - Multiplying both sides by 3, we get 7 = 3. - This is not possible, so there is no solution for y.

Conclusion

Based on the given information, there is no solution for this problem. It is not possible to determine how long each worker would take to complete the job individually.

Please let me know if there is anything else I can help you with!