Question

Бассейн можно наполнить через 4 трубы. Если открыты 2,3 и 4 трубы, то бассейн наполняется за 36 минут, если открыты 1, 3 и 4 трубы-за 45 минут, а если только 1 и 2-за 1 час. За сколько минут наполнится бассейн, если открыть все четыре трубы?

Answer 1

Problem Analysis

We have a pool that can be filled using four pipes. The time it takes to fill the pool depends on which pipes are open. We are given three scenarios: - If pipes 2, 3, and 4 are open, the pool fills in 36 minutes. - If pipes 1, 3, and 4 are open, the pool fills in 45 minutes. - If only pipes 1 and 2 are open, the pool fills in 1 hour.

We need to determine how long it will take to fill the pool if all four pipes are open.

Solution

To solve this problem, we can use a system of equations. Let's assign variables to the time it takes for each pipe to fill the pool: - Let x be the time it takes for pipe 1 to fill the pool. - Let y be the time it takes for pipe 2 to fill the pool. - Let z be the time it takes for pipe 3 to fill the pool. - Let w be the time it takes for pipe 4 to fill the pool.

From the given information, we can set up the following equations: 1. If pipes 2, 3, and 4 are open, the pool fills in 36 minutes: - y + z + w = 36.

2. If pipes 1, 3, and 4 are open, the pool fills in 45 minutes: - x + z + w = 45.

3. If only pipes 1 and 2 are open, the pool fills in 1 hour (60 minutes): - x + y = 60.

We need to solve this system of equations to find the values of x, y, z, and w.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 3, we can express x in terms of y: - x = 60 - y.

Substituting this value of x into equations 1 and 2, we get: - (60 - y) + z + w = 45 (equation 4). - y + z + w = 36 (equation 5).

Now we have two equations with three variables (y, z, and w). We can solve this system of equations using substitution or elimination.

Subtracting equation 5 from equation 4, we get: - (60 - y) - y = 45 - 36. - Simplifying, we get: 60 - 2y = 9. - Solving for y, we find: y = 25.5.

Substituting this value of y into equation 5, we get: - 25.5 + z + w = 36. - Simplifying, we find: z + w = 10.5.

Now we have two equations with two variables (z and w). We can solve this system of equations using substitution or elimination.

Since we don't have any other equations to work with, we can't determine the exact values of z and w. However, we can find their sum: - z + w = 10.5.

Answer

If all four pipes are open, the pool will fill in a time equal to the sum of z and w. From our calculations, we know that z + w = 10.5. Therefore, if all four pipes are open, the pool will fill in 10.5 minutes.

Please note that the exact values of z and w cannot be determined without additional information.

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