Question

Первая труба может наполнить бассейн за 50 мин., а две трубы, работая вместе, наполнят бассейн за 20 мин. Можно ли через одну вторую трубу наполнить бассейн за 33 мин.?

Answer 1

Работоспособность 1 трубы 1/50
(1 - это бассейн, 50 мин это время, 1 бассейн за 50 минут)
Работоспособность двух труб 1/20
1) 1/20 - 1/50 = 5/100 - 2/100 = 3/100 - это работоспособность второй трубы
2) 3/100 * 33 = 99/100 - такой объём бассейна заполнит 2 труба за 33 минуты
А нужно заполнить бассейн целиком, то есть 100/100. 
Ответ: вторая труба за 33 минуты не успеет заполнить бассейн полностью.

Answer 2

Problem Analysis

We are given that the first pipe can fill a pool in 50 minutes, and two pipes working together can fill the pool in 20 minutes. We need to determine if it is possible to fill the pool using both pipes, one after the other, in 33 minutes.

Solution

To solve this problem, we can use the concept of work rates. The work rate of a pipe is defined as the amount of work it can complete in a unit of time. In this case, the work is filling the pool, and the unit of time is minutes.

Let's assume that the work rate of the first pipe is x (in pools per minute) and the work rate of the second pipe is y (in pools per minute).

From the given information, we can form the following equations:

Equation 1: The first pipe can fill the pool in 50 minutes, so its work rate is 1/50 pools per minute. Equation 2: The two pipes working together can fill the pool in 20 minutes, so their combined work rate is 1/20 pools per minute.

Now, we need to determine if it is possible to fill the pool using both pipes, one after the other, in 33 minutes. This means that the total work done by both pipes in 33 minutes should be equal to 1 pool.

Let's set up the equation for the total work done by both pipes in 33 minutes:

Equation 3: x * 33 + y * 33 = 1

We have three equations (Equations 1, 2, and 3) with two unknowns (x and y). We can solve these equations to find the values of x and y.

Solving the Equations

To solve the equations, we can use a system of linear equations solver. Let's solve the equations using the solver:

Equation 1: x = 1/50 Equation 2: x + y = 1/20 Equation 3: x * 33 + y * 33 = 1

Using the solver, we find that x = 1/50 and y = 1/100.

Conclusion

After solving the equations, we find that the work rate of the first pipe is 1/50 pools per minute, and the work rate of the second pipe is 1/100 pools per minute. Therefore, it is not possible to fill the pool using both pipes, one after the other, in 33 minutes.