Question

Вася в одиночку красит стену за час, а один Петя красит эту стену за пол часа. За сколько минут они покрасят стену, работая вместе? Желательно с решением.

Answer 1

1 час=60 минут
пол часа =30 минут
60-30=30(мин)
ответ:за 30 минут Вася и Петя покрасят стену работая вместе

Answer 2

Problem Analysis

We are given that Vasya can paint a wall alone in 1 hour, while Petya can paint the same wall alone in 30 minutes. We need to determine how long it will take for them to paint the wall together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. In this case, the work is painting the wall, and the time is measured in minutes.

Let's denote Vasya's work rate as V (in wall per minute) and Petya's work rate as P (in wall per minute). We can calculate their work rates using the following formulas:

V = 1 wall / 60 minutes (since Vasya can paint the wall alone in 1 hour, which is equal to 60 minutes)

P = 1 wall / 30 minutes (since Petya can paint the wall alone in 30 minutes)

To find the combined work rate when they work together, we can add their individual work rates:

V + P = (1 wall / 60 minutes) + (1 wall / 30 minutes)

Simplifying the equation:

V + P = (2 walls / 60 minutes) + (1 wall / 60 minutes) = 3 walls / 60 minutes = 1 wall / 20 minutes

Therefore, when Vasya and Petya work together, their combined work rate is 1 wall per 20 minutes.

To find the time it will take for them to paint the wall together, we can use the formula:

Time = 1 wall / Combined work rate

Substituting the value of the combined work rate:

Time = 1 wall / (1 wall / 20 minutes) = 20 minutes

Therefore, it will take Vasya and Petya 20 minutes to paint the wall together.

Answer

Vasya and Petya will paint the wall together in 20 minutes.

Verification

To verify the solution, we can calculate the work done by Vasya and Petya individually and check if it matches the total work required to paint the wall.

Vasya's work rate is 1 wall per 60 minutes, so in 20 minutes, he will complete:

Vasya's work = (1 wall / 60 minutes) * 20 minutes = 1/3 wall

Petya's work rate is 1 wall per 30 minutes, so in 20 minutes, he will complete:

Petya's work = (1 wall / 30 minutes) * 20 minutes = 2/3 wall

The total work done by Vasya and Petya together is:

Total work = Vasya's work + Petya's work = 1/3 wall + 2/3 wall = 1 wall

The total work matches the work required to paint the wall, which confirms that the solution is correct.

Conclusion

Vasya and Petya will paint the wall together in 20 minutes.