Question

Один учитель проверяет тетради за 3 часа , другой за 4 часа. За сколько времени проверят тетради учителя , работая вместе ( кол-во тетрадей неизвестно и не меняется).

Answer 1

1:3=1/3 - производительность 1
1:4=1/4 - производительность 2
1/4+1/3=7/12(ч.) =35мин.

Answer 2

Problem Analysis

We are given that one teacher can check notebooks in 3 hours and another teacher can check them in 4 hours. We need to find out how long it will take for both teachers to check the notebooks together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. In this case, the work is checking the notebooks, and the time is the number of hours.

Let's assume that the first teacher's work rate is x notebooks per hour, and the second teacher's work rate is y notebooks per hour.

According to the problem, the first teacher can check all the notebooks in 3 hours, so their work rate is x = 1/3 notebooks per hour.

Similarly, the second teacher can check all the notebooks in 4 hours, so their work rate is y = 1/4 notebooks per hour.

When the two teachers work together, their work rates are additive. So the combined work rate is x + y notebooks per hour.

To find the time it takes for both teachers to check the notebooks together, we can use the formula:

Time = Total work / Combined work rate

Since the total work is the number of notebooks, and the combined work rate is x + y notebooks per hour, we can rewrite the formula as:

Time = Total notebooks / (x + y)

Since the number of notebooks is not given, we cannot determine the exact time it will take for both teachers to check the notebooks together. However, we can provide a general formula to calculate the time based on the number of notebooks.

Let's denote the total number of notebooks as N. Then the formula becomes:

Time = N / (x + y)

Now, let's summarize the solution:

1. The first teacher's work rate is x = 1/3 notebooks per hour. 2. The second teacher's work rate is y = 1/4 notebooks per hour. 3. The combined work rate of both teachers is x + y notebooks per hour. 4. The time it takes for both teachers to check the notebooks together is N / (x + y) hours, where N is the total number of notebooks.

Please note that the exact time it will take for both teachers to check the notebooks together cannot be determined without knowing the total number of notebooks.

I hope this explanation helps! Let me know if you have any further questions.