Question

Первая бригада плотников может построить дом за 7 дней,вторая за 6 дней,а третья за 14.После того как первые два дня работали первая и вторая бригады вместе,к ним присоединилась третья.За сколько дней будет построен дом?

Answer 1

1. 1:7=1/1•1/7=1/7-сколько в день строит 1 бригада
2. 1:6=1/1•1/6=1/6-сколько в день строит 2 бригада
3. 1:14=1/1•1/14=1/14-сколько в день строит 3 бригада
4. (1/7+1/6)•2=(6/42+7/42)•2=13/42•2/1=13/21-построили 1 и 2 бригада за 2 дня
5. 1-13/21=21/21-13/21=8/21-осталось достроить
6. 8/21:(1/6+1/7+1/14)=8/21:(7/42+6/42+3/42)=8/21:16/42=8/21•42/16=2/2=1-за столько дней дострят дом
7. 1+3=4-за столько дней будет выполнена работа

Answer 2

Problem Analysis

We are given three teams of carpenters: the first team can build a house in 7 days, the second team can build a house in 6 days, and the third team can build a house in 14 days. After the first two days, the third team joins the first two teams. We need to determine how many days it will take to complete the construction of the house.

Solution

To solve this problem, we can calculate the combined work rate of the three teams and use it to determine the number of days required to complete the construction.

Let's assume that the work rate of the first team is x houses per day, the work rate of the second team is y houses per day, and the work rate of the third team is z houses per day.

From the given information, we know that: - The first team can build a house in 7 days, so their work rate is 1/7 houses per day. - The second team can build a house in 6 days, so their work rate is 1/6 houses per day. - The third team can build a house in 14 days, so their work rate is 1/14 houses per day.

After the first two days, the first and second teams work together, so their combined work rate is (1/7 + 1/6) houses per day.

When the third team joins, the combined work rate of all three teams is (1/7 + 1/6 + 1/14) houses per day.

To find the number of days required to complete the construction, we can set up the following equation:

2 * (1/7 + 1/6) + x = 1

Simplifying the equation, we get:

2 * (13/42) + x = 1

Solving for x, we find:

x = 1 - 2 * (13/42)

Now, we can substitute the value of x into the equation for the combined work rate of all three teams:

1/7 + 1/6 + 1/14 + (1 - 2 * (13/42)) = 1/d

Simplifying the equation, we get:

1/d = 1/7 + 1/6 + 1/14 + (1 - 2 * (13/42))

Solving for d, we can find the number of days required to complete the construction.

Let's calculate the value of d.

Calculation

Using the equation 1/d = 1/7 + 1/6 + 1/14 + (1 - 2 * (13/42)), we can calculate the value of d.

1/d = 1/7 + 1/6 + 1/14 + (1 - 2 * (13/42))

1/d = 6/42 + 7/42 + 3/42 + (42/42 - 26/42)

1/d = 16/42 + 16/42

1/d = 32/42

d = 42/32

d = 1.3125

Since we cannot have a fraction of a day, we round up to the nearest whole number.

Therefore, it will take approximately 2 days to complete the construction of the house.

Answer

The house will be built in approximately 2 days.