Question

Басейн наповнюється через дві труби за 6 годин. Через першу трубу окремо він наповнюється на 9 годин швидше, ніж через другу. За який час басейн може наповнитися через кожну трубу окремо?

Answer 1

1. басейн наповнюється через дві труби за 6 годин ⇒ 
$\frac{1}{x+y} =6$
Продуктивність через першу трубу - х л/год.
Продуктивність через другу трубу - у л./год.
2. Через першу трубу окремо він наповнюється на 9 годин швидше, ніж через другу ⇒
$\frac{1}{y} - \frac{1}{x} =9$
3. $\left \{ {{ \frac{1}{x+y} =6} \atop { \frac{1}{y} - \frac{1}{x} =9}} \right.$ ⇒
$\left \{ {{x= \frac{1}{6} } \atop {y= \frac{1}{9} }} \right.$ ⇒
t₁=9 год.
t₂=18 год.

Answer 2

Problem Analysis

We are given that a pool is being filled through two pipes, and it takes 6 hours to fill the pool using both pipes. Additionally, we are told that the first pipe fills the pool 9 hours faster than the second pipe. We need to determine how long it would take to fill the pool using each pipe separately.

Solution

Let's assume that the time it takes to fill the pool using the second pipe is x hours.

According to the given information, the first pipe fills the pool 9 hours faster than the second pipe. Therefore, the time it takes to fill the pool using the first pipe is x + 9 hours.

We know that the combined time it takes to fill the pool using both pipes is 6 hours. Therefore, we can set up the following equation:

1/(x + 9) + 1/x = 1/6

To solve this equation, we can find a common denominator and simplify:

6x + 54 + 6x = x(x + 9)

12x + 54 = x^2 + 9x

x^2 - 3x - 54 = 0

Now we can solve this quadratic equation. Factoring or using the quadratic formula, we find that x = -6 or x = 9. Since time cannot be negative, we discard the solution x = -6.

Therefore, the time it takes to fill the pool using the second pipe is 9 hours, and the time it takes to fill the pool using the first pipe is 9 + 9 = 18 hours.

Answer

The pool can be filled through the first pipe in 18 hours and through the second pipe in 9 hours.