Question

В библиотеке надо переплести 18 00 тысяч книг одна мастерская может выполнить работу за три дня а другая за 6 дней за сколько дней переплетут все книги обе мастерские если будет работать одновременно математика 4 класс

Answer 1

Надеюсь понятно написано. Условие нужно?

Answer 2

Problem Analysis

We have two workshops that can bind books. One workshop can complete the job in 3 days, while the other workshop takes 6 days. We need to determine how many days it will take for both workshops to bind all the books if they work simultaneously.

Solution

To find the number of days it will take for both workshops to bind all the books, we can calculate the least common multiple (LCM) of 3 and 6. The LCM represents the smallest positive integer that is divisible by both 3 and 6.

The LCM of 3 and 6 is 6. Therefore, it will take 6 days for both workshops to bind all the books if they work simultaneously.

Answer: 6 days.

Explanation

When the two workshops work simultaneously, the workshop that takes 3 days will bind books at a rate of 1/3 books per day, and the workshop that takes 6 days will bind books at a rate of 1/6 books per day. Together, they will bind books at a rate of 1/3 + 1/6 = 1/2 books per day.

Since there are 18,000 books to bind, it will take 18,000 / (1/2) = 36,000 days to bind all the books.

However, since the two workshops are working simultaneously, they will bind books twice as fast. Therefore, it will take 36,000 / 2 = 18,000 days for both workshops to bind all the books.

Hence, it will take 6 days for both workshops to bind all the books if they work simultaneously.

Example Calculation

Let's consider a smaller example to illustrate the calculation. Suppose there are only 6 books to bind.

- Workshop A can bind books in 3 days, so it binds 6/3 = 2 books per day. - Workshop B can bind books in 6 days, so it binds 6/6 = 1 book per day.

When both workshops work simultaneously, they bind books at a rate of 2 + 1 = 3 books per day. Therefore, it will take 6/3 = 2 days for both workshops to bind all 6 books.

Conclusion

In conclusion, if both workshops work simultaneously, it will take 6 days for them to bind all 18,000 books.

Please let me know if you need any further assistance.