Question

одна бригада может выполнить некоторую работу за 24 дня , вторая работает в 1,5 раза медленнее, третья - так же, как и первая. за сколько дней выполнит эту работу все три бригады, работая вместе?

Answer 1

Problem Analysis

We are given three brigades that can complete a certain task. The first brigade can complete the task in 24 days. The second brigade works 1.5 times slower than the first brigade, and the third brigade works at the same speed as the first brigade. We need to determine how many days it will take for all three brigades to complete the task when working together.

Solution

To solve this problem, we can calculate the work rate of each brigade and then combine their rates to find the total work rate when they work together. Finally, we can use the total work rate to calculate the number of days required to complete the task.

Let's denote the work rate of the first brigade as R1 (work per day), the work rate of the second brigade as R2, and the work rate of the third brigade as R3. We know that the second brigade works 1.5 times slower than the first brigade, so R2 = R1 / 1.5. The third brigade works at the same speed as the first brigade, so R3 = R1.

To find the total work rate when all three brigades work together, we can add their individual work rates: Total Work Rate = R1 + R2 + R3.

Finally, we can use the total work rate to calculate the number of days required to complete the task. Let's denote the number of days required as D. We know that Total Work Rate = 1 / D (work per day), so we can solve for D using the equation: 1 / D = Total Work Rate.

Let's calculate the values step by step.

Calculation

1. Calculate the work rate of the first brigade (R1): - Given: First brigade completes the task in 24 days. - Work rate is the reciprocal of the time taken: R1 = 1 / 24.

2. Calculate the work rate of the second brigade (R2): - Given: Second brigade works 1.5 times slower than the first brigade. - R2 = R1 / 1.5.

3. Calculate the work rate of the third brigade (R3): - Given: Third brigade works at the same speed as the first brigade. - R3 = R1.

4. Calculate the total work rate when all three brigades work together: - Total Work Rate = R1 + R2 + R3.

5. Calculate the number of days required to complete the task (D): - 1 / D = Total Work Rate. - Solve for D: D = 1 / Total Work Rate.

Let's perform the calculations.

Calculation Results

1. Work rate of the first brigade (R1): - R1 = 1 / 24.

2. Work rate of the second brigade (R2): - R2 = R1 / 1.5.

3. Work rate of the third brigade (R3): - R3 = R1.

4. Total work rate when all three brigades work together: - Total Work Rate = R1 + R2 + R3.

5. Number of days required to complete the task (D): - D = 1 / Total Work Rate.

Let's calculate the values.

Calculation Results

1. Work rate of the first brigade (R1): - R1 = 1 / 24 = 0.0417.

2. Work rate of the second brigade (R2): - R2 = R1 / 1.5 = 0.0417 / 1.5 = 0.0278.

3. Work rate of the third brigade (R3): - R3 = R1 = 0.0417.

4. Total work rate when all three brigades work together: - Total Work Rate = R1 + R2 + R3 = 0.0417 + 0.0278 + 0.0417 = 0.1111.

5. Number of days required to complete the task (D): - D = 1 / Total Work Rate = 1 / 0.1111 = 9.

Therefore, it will take all three brigades working together 9 days to complete the task.

Answer

All three brigades, working together, will complete the task in 9 days.

Please let me know if anything is unclear or if you need further assistance!