Question

Решите задачу. Игорь и Паша красят забор за 10 ч. Паша и Володя красят этот же забор за 15 часов, а Володя и Игорь- за 18 часов. За сколько минут мальчики покрасят забор, работая втроём? помогите пжл срочноо

Answer 1

Х+у=10, у+а=15, х+а=18.
Сложим все уравнения:
х+у+у+а+х+а=10+15+18
2(х+у+а)=43
х+у+а=21,5
21,5ч=1290минут.

Answer 2

Problem Analysis

We are given that Igor and Pasha can paint a fence in 10 hours, Pasha and Volodya can paint the same fence in 15 hours, and Volodya and Igor can paint the fence in 18 hours. We need to find out how many minutes it will take for all three boys to paint the fence together.

Solution

Let's assume that the efficiency of Igor, Pasha, and Volodya is represented by the variables I, P, and V, respectively. We can calculate their individual rates of work using the formula:

Rate of work = 1 / Time taken

From the given information, we can set up the following equations:

1. Igor and Pasha can paint the fence in 10 hours: - (I + P) = 1/10

2. Pasha and Volodya can paint the fence in 15 hours: - (P + V) = 1/15

3. Volodya and Igor can paint the fence in 18 hours: - (V + I) = 1/18

To find the rate at which all three boys can paint the fence together, we add up the rates of work for each pair of boys:

Rate of work for all three boys = I + P + V

Now, we can solve the system of equations to find the values of I, P, and V.

Calculation

Let's solve the system of equations:

1. (I + P) = 1/10 2. (P + V) = 1/15 3. (V + I) = 1/18

Adding equations 1, 2, and 3, we get:

2(I + P + V) = 1/10 + 1/15 + 1/18

Simplifying the right side of the equation:

2(I + P + V) = (9 + 6 + 5) / 90

2(I + P + V) = 20 / 90

2(I + P + V) = 1 / 4.5

(I + P + V) = 1 / (2 * 4.5)

(I + P + V) = 1 / 9

Therefore, the rate of work for all three boys is 1/9.

To find the time it takes for all three boys to paint the fence, we can use the formula:

Time taken = 1 / Rate of work

Substituting the rate of work (1/9) into the formula:

Time taken = 1 / (1/9)

Time taken = 9

Since there are 60 minutes in an hour, the boys will take 9 * 60 = 540 minutes to paint the fence together.

Answer

The boys will take 540 minutes to paint the fence together when working as a team.