Question

Якщо відкрити одночасно дві труби, то басейн буде наповне- но водою за 12 год. Якщо спочатку наповнювати басейн тільки через першу трубу протягом 5 год, а потім тільки через другу протягом 9 год, то водою буде наповнено половину басейну. За скільки годин можна наповнити басейн через кожну трубу?​

Answer 1

Відповідь:

Перша труба за 16 год.

Друга труба за 48 год.

Пояснення:

На фото:

Answer 2

Нехай х - час, за який можна наповнити басейн через першу трубу, а у - час, за який можна наповнити басейн через другу трубу.

Тоді за умовою задачі маємо таку систему рівнянь:

1/х + 1/у = 1/12 (за одночасного наповнення обох трубами) 5/х + 9/у = 1/2 (за послідовного наповнення басейну)

Розв'язавши цю систему рівнянь, отримаємо, що x = 15 годин, y = 20 годин.

Отже, через першу трубу басейн можна наповнити за 15 годин, а через другу - за 20 годин.

Answer 3

Problem Analysis

We are given that if two pipes are opened simultaneously, they can fill a pool with water in 12 hours. However, if the pool is first filled through one pipe for 5 hours and then through the other pipe for 9 hours, only half of the pool is filled. We need to determine how long it would take to fill the pool through each pipe individually.

Solution

Let's assume that the rate at which the first pipe fills the pool is x units per hour, and the rate at which the second pipe fills the pool is y units per hour.

According to the given information, if both pipes are opened simultaneously, they can fill the pool in 12 hours. This means that the combined rate of both pipes is equal to the pool's capacity divided by 12 hours:

x + y = pool capacity / 12 ---(Equation 1)

We are also given that if the pool is first filled through the first pipe for 5 hours and then through the second pipe for 9 hours, only half of the pool is filled. This means that the amount of water filled by the first pipe in 5 hours plus the amount of water filled by the second pipe in 9 hours is equal to half of the pool's capacity:

5x + 9y = pool capacity / 2 ---(Equation 2)

To find the time it takes to fill the pool through each pipe individually, we can solve these two equations simultaneously.

Solving the Equations

To solve the equations, we can use the method of substitution. Rearranging Equation 1, we get:

x = pool capacity / 12 - y ---(Equation 3)

Substituting Equation 3 into Equation 2, we get:

5(pool capacity / 12 - y) + 9y = pool capacity / 2

Simplifying the equation:

(5/12)pool capacity - 5y + 9y = (1/2)pool capacity

Combining like terms:

(5/12)pool capacity + 4y = (1/2)pool capacity

Multiplying both sides by 12 to eliminate the fractions:

5pool capacity + 48y = 6pool capacity

Rearranging the equation:

y = (1/6)(pool capacity) ---(Equation 4)

Substituting Equation 4 into Equation 3, we get:

x = pool capacity / 12 - (1/6)(pool capacity)

Simplifying the equation:

x = (1/12)(pool capacity) ---(Equation 5)

Answer

From the above calculations, we can conclude that: - The first pipe can fill the pool in (1/12)th of the time it takes to fill the pool when both pipes are opened simultaneously. - The second pipe can fill the pool in (1/6)th of the time it takes to fill the pool when both pipes are opened simultaneously.

Therefore, to fill the pool through each pipe individually: - The first pipe will take (1/12)th of 12 hours, which is 1 hour. - The second pipe will take (1/6)th of 12 hours, which is 2 hours.

So, it will take 1 hour to fill the pool through the first pipe and 2 hours to fill the pool through the second pipe.

Conclusion

To summarize: - The first pipe can fill the pool in 1 hour. - The second pipe can fill the pool in 2 hours.

Please let me know if anything is unclear or if you need further assistance!