Question

Бассейн заполняется через две трубы. Если открыть их одновременно, бассейн заполнится за 6 часов. Через первую трубу можно заполнить бассейн на 5 часов быстрее чем через вторую. За какое время бассейн заполнится через первую трубу?

Answer 1

Ответ:

время заполнения 1ой трубой бассейна - 10 часов

Answer 2

#### Problem Analysis We are given that a pool is being filled through two pipes. If both pipes are opened simultaneously, the pool will be filled in 6 hours. It is also mentioned that the first pipe can fill the pool 5 hours faster than the second pipe. We need to determine how long it will take to fill the pool using only the first pipe. #### Solution Let's assume that the second pipe takes x hours to fill the pool. Since the first pipe can fill the pool 5 hours faster than the second pipe, it will take (x - 5) hours to fill the pool using the first pipe. According to the given information, if both pipes are opened simultaneously, the pool will be filled in 6 hours. This means that in 1 hour, both pipes together can fill 1/6th of the pool. In 1 hour, the first pipe can fill 1/(x - 5) of the pool, and the second pipe can fill 1/x of the pool. Together, they can fill 1/6th of the pool. So, we can set up the following equation: 1/(x - 5) + 1/x = 1/6 To solve this equation, we can multiply both sides by 6x(x - 5) to eliminate the denominators: 6x + 6(x - 5) = x(x - 5) Simplifying the equation: 6x + 6x - 30 = x^2 - 5x Rearranging the equation: x^2 - 17x + 30 = 0 Now we can solve this quadratic equation to find the value of x. #### Quadratic Equation Solution Using the quadratic formula, we can find the solutions for x: x = (-b ± √(b^2 - 4ac)) / (2a) For our equation x^2 - 17x + 30 = 0, the values of a, b, and c are: a = 1 b = -17 c = 30 Substituting these values into the quadratic formula: x = (-(-17) ± √((-17)^2 - 4 * 1 * 30)) / (2 * 1) Simplifying the equation: x = (17 ± √(289 - 120)) / 2 x = (17 ± √169) / 2 x = (17 ± 13) / 2 So, we have two possible solutions for x: x1 = (17 + 13) / 2 = 15 x2 = (17 - 13) / 2 = 2 Since the second pipe takes 2 hours to fill the pool, the first pipe will take (2 - 5) = -3 hours to fill the pool. However, negative time is not possible, so we discard this solution. Therefore, the pool will be filled through the first pipe in 15 - 5 = **10 hours**. #### Answer The pool will be filled through the first pipe in **10 hours**.