Question

Библиотеке надо переплести 960 книг. Одна переплётная мастерская может выполнить эту работу за 16, другая- за 24 и третья- за 48 дней. В какой срок могут выполнить эту работу три мастерские, работая одновременно, и сколько книг успеет переплести каждая мастерская? Можно ли распределить книги между мастерскими так, чтобы эта работа была выполнена за более короткий срок?

Answer 1

Блин,я помню,что решала эту задачу тоже,но точно решение не помню и на все вопросы ответить не смогу так,что лучше потом проверь,но по моему 
1)960/16=60(к.) переплетает в день 1 мастерская
2)960/24=40(к.) переплетает в день 2 мастерская 
3)969/48=20(к.) переплетает в день 3 мастерская 
4)60+40+20=120(к.) могут переплести в день все мастерские
5)960:120=8(д.) нужно дней,если будут работать одновременно
6)60*8=480(к.) успеет переплести 1 мастерская 
7)40*8=320(к.) успеет переплести 2 мастерская
8)20*8=160(к,) успеет переплести 3 мастерская

Answer 2

Problem Analysis

We have three bookbinding workshops that can complete the task of binding 960 books. The first workshop can complete the task in 16 days, the second workshop in 24 days, and the third workshop in 48 days. We need to determine how long it will take for all three workshops to complete the task if they work simultaneously. Additionally, we need to calculate the number of books each workshop will be able to bind. Finally, we need to determine if it is possible to distribute the books among the workshops in a way that allows the task to be completed in a shorter time.

Solution

To find the time it will take for all three workshops to complete the task when working simultaneously, we can calculate the least common multiple (LCM) of the individual completion times for each workshop. The LCM will give us the total time required for all workshops to finish the task together.

To calculate the number of books each workshop will bind, we can divide the total number of books (960) by the respective completion times for each workshop.

Let's calculate the answers step by step.

Calculation

1. Calculate the LCM of 16, 24, and 48 to find the total time required for all three workshops to complete the task together.

The LCM of 16, 24, and 48 is 48. Therefore, it will take all three workshops 48 days to complete the task when working simultaneously.

2. Calculate the number of books each workshop will bind.

- Workshop 1: 960 books / 16 days = 60 books per day - Workshop 2: 960 books / 24 days = 40 books per day - Workshop 3: 960 books / 48 days = 20 books per day

3. Determine if it is possible to distribute the books among the workshops in a way that allows the task to be completed in a shorter time.

Since the completion times of the workshops are not divisible by each other, it is not possible to distribute the books in a way that would allow the task to be completed in a shorter time.

Answer

- All three workshops working simultaneously will complete the task in 48 days. - Workshop 1 will bind 60 books per day. - Workshop 2 will bind 40 books per day. - Workshop 3 will bind 20 books per day.

It is not possible to distribute the books among the workshops in a way that would allow the task to be completed in a shorter time.

Please let me know if there is anything else I can help you with!