Question

Одна бригада может выполнить некоторый заказ за 10 дней , а другая за 15 дней . За сколько дней обе бригады выполнят заказ работая вместе?

Answer 1

за 6 дней

производительность первой команды одна десятая, производительность второй - одна пятнадцатая, складываем их и получается пять тридцатых. сокрашаем. получается одна шестая. это значит что они смогут сделать один заказ за 6 дней

Answer 2

Problem Analysis

We have two brigades that can complete a certain order in 10 days and 15 days, respectively. We need to determine how many days it will take for both brigades to complete the order when working together.

Solution

To solve this problem, we can use the concept of work rates. The work rate of a brigade is the amount of work it can complete in a unit of time. Let's assume that the work rate of the first brigade is x and the work rate of the second brigade is y.

According to the problem, the first brigade can complete the order in 10 days, so its work rate is 1/10 of the order per day. Similarly, the second brigade can complete the order in 15 days, so its work rate is 1/15 of the order per day.

When both brigades work together, their work rates are additive. Therefore, the combined work rate of both brigades is x + y.

Now, let's set up an equation to find the number of days it will take for both brigades to complete the order when working together. We can use the formula:

1/(x + y) = 1/10 + 1/15

Simplifying this equation will give us the value of x + y, which represents the combined work rate of both brigades. We can then calculate the number of days it will take for both brigades to complete the order by taking the reciprocal of x + y.

Let's solve the equation to find the answer.

Calculation

To find the value of x + y, we can solve the equation:

1/(x + y) = 1/10 + 1/15

Multiplying both sides of the equation by 150(x + y) to eliminate the denominators, we get:

150 = 15(x + y) + 10(x + y)

Simplifying the equation, we have:

150 = 25(x + y)

Dividing both sides of the equation by 25, we get:

6 = x + y

So, the combined work rate of both brigades is 6.

To find the number of days it will take for both brigades to complete the order, we can use the formula:

1/(x + y) = 1/d

Substituting the value of x + y as 6, we have:

1/6 = 1/d

Cross-multiplying the equation, we get:

d = 6

Therefore, it will take both brigades 6 days to complete the order when working together.

Answer

Both brigades will complete the order in 6 days when working together.