Question

Через одну трубу бассейн наполняется на 6 часов быстрее, чем через другую. Если открыть обе трубы одновременно бассейн наполнится за 4 часа. За какое время заполнится бассейн через каждую из труб, открытых по отдельности?​

Answer 1

Пошаговое объяснение:

Пусть х ч-время наполнения бассейна через 1 трубу в отдельности, тогда (х-6) ч-время наполнения через 2 трубу. По условию задачи составим уравнение:  

4/x+4/(x-6)=1  

4(x-6)+4x-x(x-6)=0  

x²-14x+24=0  

x1=12  

x2=2-не подходит. т. к. х-6<0  

Ответ: 12 ч.

Answer 2

#### Problem Analysis We are given that one pipe fills a pool in 6 hours faster than another pipe. When both pipes are opened simultaneously, the pool is filled in 4 hours. We need to determine how long it would take to fill the pool using each pipe separately. #### Solution Let's assume that the slower pipe fills the pool in x hours. This means that the faster pipe fills the pool in (x - 6) hours. When both pipes are opened simultaneously, they can fill the pool in 4 hours. This means that their combined rate of filling the pool is 1/4 of the pool per hour. Using this information, we can set up the following equation: 1/x + 1/(x - 6) = 1/4 To solve this equation, we can multiply through by 4x(x - 6) to eliminate the fractions: 4(x - 6) + 4x = x(x - 6) Simplifying the equation: 4x - 24 + 4x = x^2 - 6x Combining like terms: 8x - 24 = x^2 - 6x Rearranging the equation: x^2 - 14x + 24 = 0 Now we can solve this quadratic equation to find the value of x. Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a) For our equation, a = 1, b = -14, and c = 24. Calculating the discriminant: D = b^2 - 4ac = (-14)^2 - 4(1)(24) = 196 - 96 = 100 Since the discriminant is positive, we have two real solutions for x. Using the quadratic formula: x = (-(-14) ± √(100)) / (2(1)) x = (14 ± 10) / 2 We have two possible solutions: x1 = (14 + 10) / 2 = 24 / 2 = 12 x2 = (14 - 10) / 2 = 4 / 2 = 2 Therefore, the slower pipe takes 12 hours to fill the pool, and the faster pipe takes 2 hours to fill the pool. #### Answer The pool will be filled in 12 hours using the slower pipe and in 2 hours using the faster pipe when each pipe is opened separately.