Question

В бассейн ведут три трубы, каждая из которых равномерно заполняет бассейн. Если включить первые две трубы, то бассейн заполнится за 40 минут. Если первую и третью, то за 30 минут. А если вторую и третью, то за двадцать минут. Успеет ли бассейн заполнится за 18 минут, если включить все трубы?

Answer 1

Обозначим х - полный бассейн.
Тогда скорость заполнения бассейна при включенных 1-й и 2-й трубах:
v₁₂ = v₁+v₂ = x/40
скорость заполнения бассейна при включенных 1-й и 3-й трубах:
v₁₃ = v₁+v₃ = x/30
скорость заполнения бассейна при включенных 2-й и 3-й трубах:
v₂₃ = v₂+v₃ = x/20

Тогда: 2(v₁+v₂+v₃) = x/40 + x/30 + x/20
               v₁+v₂+v₃ = ((3x+4x+6x)/120):2
               v₁+v₂+v₃ = 13x/240
Таким образом, 13 бассейнов заполнятся тремя трубами за 240 минут.
То есть 1 бассейн заполнится тремя трубами за:
                           t = 240:13 ≈ 18,5 (мин)

Ответ: бассейн за 18 мин. заполниться не успеет.

Answer 2

1/(3/120+4/120+6/120):2=240/240 *240/13=57600/3120=18,4615384....

Answer 3

Problem Analysis

We are given three pipes that fill a pool. Each pipe fills the pool at a constant rate. We are given the time it takes to fill the pool when two of the pipes are turned on together. We need to determine if the pool can be filled in 18 minutes when all three pipes are turned on.

Solution

Let's assume that the rates at which the three pipes fill the pool are x, y, and z units per minute, respectively.

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

1. When the first two pipes are turned on, the pool fills up in 40 minutes: - The combined rate of the first two pipes is x + y units per minute. - The total volume of the pool is filled in 40 minutes, which is 40 * (x + y) units.

2. When the first and third pipes are turned on, the pool fills up in 30 minutes: - The combined rate of the first and third pipes is x + z units per minute. - The total volume of the pool is filled in 30 minutes, which is 30 * (x + z) units.

3. When the second and third pipes are turned on, the pool fills up in 20 minutes: - The combined rate of the second and third pipes is y + z units per minute. - The total volume of the pool is filled in 20 minutes, which is 20 * (y + z) units.

We can set up a system of equations using the above information:

Equation 1: 40 * (x + y) = V (where V is the total volume of the pool)

Equation 2: 30 * (x + z) = V

Equation 3: 20 * (y + z) = V

To determine if the pool can be filled in 18 minutes when all three pipes are turned on, we need to find the rate at which the three pipes fill the pool and check if the total volume of the pool can be filled in 18 minutes.

Let's solve the system of equations to find the values of x, y, and z.

Solution Steps

1. Solve Equation 1 for V: V = 40 * (x + y) 2. Solve Equation 2 for V: V = 30 * (x + z) 3. Solve Equation 3 for V: V = 20 * (y + z) 4. Equate the expressions for V from Equations 1, 2, and 3: - 40 * (x + y) = 30 * (x + z) = 20 * (y + z) 5. Solve the above equation to find the values of x, **