Question

Библиотеке нужно переплести книги одна мастерская может выполнить эту работу за 16 дней, вторая- за 24 дня, а третья- за 48 дней. В какой срок могут выполнить эту работу три мастерские, работая одновременно?

Answer 1

16+24=30-1ая и 2ая
30+48=70 всего

Answer 2

Problem Analysis

We have three workshops that can bind books. The first workshop can complete the job 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 job if they work simultaneously.

Solution

To find the time it takes for all three workshops to complete the job, 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 total work required to bind the books is 1 unit.

The work rate of the first workshop is 1/16 units per day, as it can complete the job in 16 days. The work rate of the second workshop is 1/24 units per day, as it can complete the job in 24 days. The work rate of the third workshop is 1/48 units per day, as it can complete the job in 48 days.

When all three workshops work simultaneously, their work rates are additive. Therefore, the combined work rate of all three workshops is:

1/16 + 1/24 + 1/48 = (3 + 2 + 1)/48 = 6/48 = 1/8 units per day.

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

Time = Work / Work Rate.

Substituting the values, we have:

Time = 1 / (1/8) = 8 days.

Therefore, it will take all three workshops working simultaneously 8 days to complete the job.

Answer: The three workshops can complete the job in 8 days if they work simultaneously.