Question

На лодочной станции надо покрасить 168 лодок.Один мастер может выполнить эту работу за 28 дней , а другой за 21 день. За сколько дней они могут выполнить эту работу , работая вместе

Answer 1

168:28=6 (лодок) за 1 день первый мастер
168:21=8 (лодок) за 1 день второй
6+8=14 (лодок) за 1 день вместе
168:14=12 (дней)
Ответ: вместе выполнят работу за 12 дней

Answer 2

Problem Analysis

We have two masters who can paint boats. One master can complete the job in 28 days, while the other can complete it in 21 days. We need to determine how many days it will take for them to complete the job if they work together.

Solution

To find the number of days it will take for the two masters to complete the job together, we can use the concept of work rates. The work rate of a person is defined as the amount of work they can complete in a unit of time.

Let's assume that the work rate of the first master is x boats per day, and the work rate of the second master is y boats per day.

According to the problem, the first master can complete the job in 28 days, so their work rate is 1/28 boats per day. Similarly, the second master can complete the job in 21 days, so their work rate is 1/21 boats per day.

When the two masters work together, their work rates are additive. So, the combined work rate is x + y boats per day.

We need to find the number of days it will take for them to complete the job when they work together. Let's assume this number of days is d.

According to the work rate formula, the work done is equal to the work rate multiplied by the time taken. In this case, the work done is equal to the total number of boats, which is 168.

So, we can set up the following equation: (x + y) * d = 168

Now, we can solve this equation to find the value of d.

Calculation

Let's solve the equation to find the value of d.

(x + y) * d = 168

Substituting the work rates of the masters: (1/28 + 1/21) * d = 168

Simplifying the equation: (3/84 + 4/84) * d = 168 7/84 * d = 168

Multiplying both sides by 84 to isolate d: 7d = 168 * 84 7d = 14112

Dividing both sides by 7 to solve for d: d = 14112 / 7 d = 2016

Answer

Therefore, it will take the two masters 2016 days to complete the job if they work together.

Please note that this is a hypothetical calculation based on the given information. The actual time required to complete the job may vary depending on various factors.

Let me know if you need any further assistance!