Question

Помогите решить задачу. Чтобы наполнить бассейн водой через одну трубу,требуется в 1,5 раза больше времени,чем для того,чтобы наполнить его через вторую трубу.Если же открыть обе трубы одновременно,то бассейн наполнится за 6 часов. За сколько часов можно наполнить бассейн через каждую трубу отдельно?

Answer 1

Пусть Х часов понадобится, чтобы заполнить бассейн через одну трубу, тогда через другую понадобится 1,5Х
уравнение:
1,5Х+Х=6
2,5Х=6
Х=6:2,5
Х=2,4 ч- через 1ую трубу
1,5*2,4=3,6 ч- через 2ую
Ответ: 2,4ч, 3,6 ч

Answer 2

Problem Analysis

We are given that it takes 1.5 times longer to fill a pool using one pipe compared to using another pipe. When both pipes are opened simultaneously, the pool is filled in 6 hours. 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 first pipe is x hours. According to the problem, it would take 1.5 times longer to fill the pool using the second pipe, so it would take 1.5x hours.

When both pipes are opened simultaneously, the pool is filled in 6 hours. This means that the combined rate of filling the pool using both pipes is 1/6 of the pool per hour.

To find the individual rates of filling the pool using each pipe separately, we can set up the following equation:

1/x + 1/(1.5x) = 1/6

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation 1/x + 1/(1.5x) = 1/6, we can multiply both sides of the equation by 6x(1.5x) to eliminate the denominators:

6(1.5x) + 6x = x(1.5x)

Simplifying the equation:

9x + 6x = 1.5x^2

15x = 1.5x^2

Dividing both sides of the equation by 1.5x:

10 = x

Therefore, it would take 10 hours to fill the pool using the first pipe and 15 hours to fill the pool using the second pipe.

Answer

To fill the pool using each pipe separately: - The first pipe would take 10 hours. - The second pipe would take 15 hours.

Please let me know if you need any further assistance!