Question

Библиотеке нужно переплести 1800 книг. Первая мастерская может выполнить эту работу за 3 дня, а вторая - за 6 дней. За сколько дней переплетут все книги обе мастерские, если будут работать одновременно? (Считать, что на переплет каждой книги расходится одинаковое время)

Answer 1

1800:3= 600 книг в 1 день делает 1 бригада
1800:6=300 книг в 1 день делает 2 бригада
600+300=900 книг в 1 день обе бригады
1800:900= за 2 дня переплетут все книги обе мастерские, если будут работать одновременно

Answer 2

Problem Analysis

We are given that there are 1800 books that need to be bound. The first workshop can bind all the books in 3 days, while the second workshop can bind all the books in 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 use the concept of work rates. The work rate is the amount of work done per unit of time.

Let's assume that the work rate of the first workshop is W1 (books per day) and the work rate of the second workshop is W2 (books per day). We need to find the combined work rate when both workshops work simultaneously.

Since the work rates are given in terms of days, we can say that the work rate of the first workshop is 1/3 books per day and the work rate of the second workshop is 1/6 books per day.

To find the combined work rate, we can add the individual work rates:

Combined work rate = W1 + W2 = 1/3 + 1/6 = 1/2 books per day

Now, we can use the combined work rate to find the number of days it will take for both workshops to bind all the books. Let's assume that it takes D days for both workshops to bind all the books.

The total work done by both workshops in D days is equal to the number of books, which is 1800:

Total work = Combined work rate * D = 1/2 * D = 1800 books

Solving this equation for D, we get:

D = 1800 / (1/2) = 3600 days

Therefore, it will take both workshops 3600 days to bind all the books if they work simultaneously.

Answer

If both workshops work simultaneously, it will take them 3600 days to bind all 1800 books.