Question

Первый рабочий может выполнить задание за 8 ч, а второй за 6ч. Они работали вместе 2 ч, а заканчивал задание один второй рабочий. Сколько времени потребовалось для выполнения этого задания

Answer 1

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Answer 2

Problem Analysis

We have two workers who can complete a task in different amounts of time. The first worker can complete the task in 8 hours, while the second worker can complete it in 6 hours. They worked together for 2 hours, and then the second worker finished the task alone. We need to determine how much time it took to complete the task.

Solution

To solve this problem, we can calculate the amount of work done by the two workers in the 2 hours they worked together and then determine how much work was left for the second worker to complete alone.

Let's denote the amount of work done by the first worker in 1 hour as W1 and the amount of work done by the second worker in 1 hour as W2.

From the given information, we know that the first worker can complete the task in 8 hours, so W1 = 1/8. Similarly, the second worker can complete the task in 6 hours, so W2 = 1/6.

In the 2 hours they worked together, the total amount of work done is 2 * (W1 + W2).

Now, let's calculate the amount of work left for the second worker to complete alone. The total amount of work required for the task is 1 (since it is a complete task).

The amount of work left for the second worker to complete alone is 1 - 2 * (W1 + W2).

To find the time required for the second worker to complete the remaining work, we can use the formula:

Time = Amount of work / Work rate

The work rate of the second worker is W2 (since the second worker is working alone).

Therefore, the time required for the second worker to complete the remaining work is:

Time = (1 - 2 * (W1 + W2)) / W2

Let's calculate this value:

Time = (1 - 2 * (1/8 + 1/6)) / (1/6)

Simplifying the expression:

Time = (1 - 2 * (7/48)) / (1/6)

Time = (1 - 7/24) / (1/6)

Time = (24/24 - 7/24) / (1/6)

Time = 17/24 / (1/6)

Time = 17/24 * 6/1

Time = 17/4

Therefore, it took the second worker 17/4 hours to complete the remaining work alone.

Answer

It took the second worker 17/4 hours to complete the remaining work alone.

Note: The answer has been calculated based on the given information and the formulas for work rate and time.