Question

Дві бригади працюючи разом, можуть виконати певне завдання за 12 год. Якщо спочатку половину роботи виконає перша бригада, а потім друга її завершить, то всю роботу буде виконано за 25 год. За скільки годин може виконати завдання кожна бригада, працюючи самостійно?

Answer 1

X1 - час для виконання всієї роботи першою бригадою
x2 - час для виконання всієї роботи другою бригадою

за 1 годину 1 бригада виконає 1/х1 роботи
за 1 годину 2 бригада виконає 1/х2 роботи
всю роботу виконають за 12 годин

1/(1/х1+1/х2)=12
х1+10=х2

———————

х1*х2=12*(х1+х2)
х1+10=х2

———————

х1*х1+10х1=12*х1+12*х1+12*10

———————

х1*х1-14х1-120=0
x1=20 - це відповідь
x1=-6 - а це сторонній корінь

Answer 2

Problem Analysis

We are given that two brigades working together can complete a task in 12 hours. If the first brigade completes half of the work and then the second brigade completes the remaining half, the task will be completed in 25 hours. We need to determine how long each brigade would take to complete the task individually.

Solution

Let's assume that the first brigade can complete the task in x hours, and the second brigade can complete the task in y hours.

According to the given information, when both brigades work together, they can complete the task in 12 hours. This means that their combined work rate is 1/12 of the task per hour.

When the first brigade completes half of the work, it means that they have completed 1/2 of the task. Similarly, when the second brigade completes the remaining half, it means that they have completed another 1/2 of the task.

According to the given information, if the first brigade completes half of the work and then the second brigade completes the remaining half, the task will be completed in 25 hours. This means that their combined work rate is 1/25 of the task per hour.

Using the work rate formula (work rate = amount of work / time), we can set up the following equations:

For both brigades working together: 1/12 = 1 / x + 1 / y

For the first brigade completing half of the work and the second brigade completing the remaining half: 1/25 = 1 / x + 1 / y

We can solve these equations to find the values of x and y, which represent the number of hours each brigade would take to complete the task individually.

Let's solve these equations:

1/12 = 1 / x + 1 / y ----(1) 1/25 = 1 / x + 1 / y ----(2)

Subtracting equation (2) from equation (1), we get:

1/12 - 1/25 = 1 / x + 1 / y - 1 / x - 1 / y

Simplifying the equation:

(25 - 12) / (12 * 25) = (x + y - x - y) / (x * y)

13 / 300 = 0

This equation is not possible, as it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

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