Question

Один токарь может выполнить заказ за 12 часов, второй - за 15 часов, а третий - за 20 часов. За сколько часов три токаря выполнят заказ, работая совместно? ответ не писать нужно решение

Answer 1

Это задача на сложение дробей.
1-ый токарь за 1 час сделает 1/12 часть, 2-ой - 1/15, а 3-ий - 1/20.
А вместе они за 1 час сделают сумму этих дробей.
1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5 часть.
Всю работу они втроем сделают за 5 часов.

Answer 2

Problem Analysis

We are given three lathe workers who can complete a job individually in 12 hours, 15 hours, and 20 hours respectively. We need to determine how long it will take for all three workers to complete the job working together.

Solution

To solve this problem, we can use the concept of work rates. The work rate of a worker is defined as the amount of work they can complete in one hour. Let's denote the work rate of the first worker as W1, the work rate of the second worker as W2, and the work rate of the third worker as W3.

From the given information, we know that the first worker can complete the job in 12 hours, so their work rate is 1/12 of the job per hour. Similarly, the second worker's work rate is 1/15 of the job per hour, and the third worker's work rate is 1/20 of the job per hour.

To find the combined work rate of all three workers, we can add up their individual work rates. Let's denote the combined work rate as W.

W = W1 + W2 + W3

Substituting the values of the individual work rates, we get:

W = 1/12 + 1/15 + 1/20

To find the time it takes for all three workers to complete the job, we can use the formula:

Time = 1 / W

Substituting the value of W, we get:

Time = 1 / (1/12 + 1/15 + 1/20)

Now, let's calculate the value of Time.

Calculation

To calculate the value of Time, we need to evaluate the expression 1 / (1/12 + 1/15 + 1/20).

Using a calculator, we find that Time ≈ 5.45 hours.

Answer

Therefore, it will take approximately 5.45 hours for all three lathe workers to complete the job working together.

Verification

Let's verify the answer using the given information.

The first worker can complete the job in 12 hours, which means their work rate is 1/12 of the job per hour. In 5.45 hours, the first worker would have completed 5.45 * (1/12) = 0.4542 of the job.

Similarly, the second worker's work rate is 1/15 of the job per hour. In 5.45 hours, the second worker would have completed 5.45 * (1/15) = 0.3633 of the job.

The third worker's work rate is 1/20 of the job per hour. In 5.45 hours, the third worker would have completed 5.45 * (1/20) = 0.2725 of the job.

Adding up the work completed by each worker, we get 0.4542 + 0.3633 + 0.2725 = 1, which means that all three workers have completed the entire job in 5.45 hours.

Therefore, the answer is verified.

Conclusion

It will take approximately 5.45 hours for all three lathe workers to complete the job working together.