Question

Библиотеке надо переплести 900 книг.Первая мастерская может выполнить эту работу за 10 дней,а вторая за 15 дней.За сколько дней выполнят эту работу мастерские , если будут работать вместе?

Answer 1

900÷10=90 книг в день, производительность первой мастерской
900÷15=60 книг в день, производительность второй мастерской
90+60=150 книг в день, общая производительность
900÷150=6 дней
за 6 дней выполнят работу две мастерские вместе

Answer 2

Problem Analysis

We are given that there are two workshops that can bind books. The first workshop can bind 900 books in 10 days, while the second workshop can bind the same number of books in 15 days. We need to determine how many days it will take for both workshops to complete the binding job if they work together.

Solution

To solve this problem, we can use the concept of work rates. The work rate of a workshop is defined as the number of books it can bind in a given time period. Let's denote the work rate of the first workshop as W1 (books per day) and the work rate of the second workshop as W2 (books per day).

From the given information, we know that the first workshop can bind 900 books in 10 days, so its work rate is:

W1 = 900 books / 10 days = 90 books per day.

Similarly, the second workshop can bind 900 books in 15 days, so its work rate is:

W2 = 900 books / 15 days = 60 books per day.

Now, let's assume that it takes D days for both workshops to complete the binding job when they work together. Since they are working together, their work rates will add up:

W1 + W2 = Total work rate.

Substituting the values of W1 and W2, we get:

90 books per day + 60 books per day = Total work rate.

Simplifying the equation, we find that the total work rate is:

150 books per day.

Since the total work rate is the combined work rate of both workshops, we can calculate the number of days it will take for them to complete the binding job by dividing the total number of books (900) by the total work rate (150 books per day):

D = 900 books / 150 books per day = 6 days.

Therefore, it will take both workshops 6 days to complete the binding job if they work together.

Answer

If the first workshop can bind 900 books in 10 days and the second workshop can bind the same number of books in 15 days, then it will take both workshops 6 days to complete the binding job if they work together.