Question

Через первую трубу водоем можно наполнить за 6 часов,а через вторую в 1/2 часа быстрее, чем в первой. За сколько часов наполнится водоем при совместной работе этих труб?​

Answer 1

Ответ:

1)6:2=3(ч)-время за которое можно наполнить водоём через 2 трубу.

2)3+6=9(ч)-общее время работы труб.

3)9:2=4,5=4ч30мин.

ответ:чтобы наполнить водоём понадобится 4ч30мин.

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a reservoir in 6 hours, and the other can fill it in 1/2 hour less than the first pipe. We need to determine how long it will take to fill the reservoir when both pipes are working together.

Solution

Let's assume that the first pipe can fill the reservoir in x hours. According to the problem, the second pipe can fill the reservoir in 1/2 hour less than the first pipe. Therefore, the second pipe can fill the reservoir in (x - 1/2) hours.

When both pipes are working together, their combined rate of filling the reservoir is the sum of their individual rates. The rate of the first pipe is 1/x of the reservoir per hour, and the rate of the second pipe is 1/(x - 1/2) of the reservoir per hour.

To find the time it takes to fill the reservoir when both pipes are working together, we can set up the following equation:

1/x + 1/(x - 1/2) = 1/t

Where t is the time it takes to fill the reservoir when both pipes are working together.

To solve this equation, we can multiply through by the least common denominator, which is 2x(x - 1/2):

2(x - 1/2) + 2x = x(x - 1/2)

Simplifying the equation:

2x - 1 + 2x = x^2 - x/2

4x - 1 = x^2 - x/2

8x - 2 = 2x^2 - x

2x^2 - 9x + 2 = 0

Using the quadratic formula, we can solve for x:

x = (-(-9) ± sqrt((-9)^2 - 4(2)(2)))/(2(2))

x = (9 ± sqrt(81 - 16))/4

x = (9 ± sqrt(65))/4

Since the time cannot be negative, we take the positive value:

x = (9 + sqrt(65))/4

Therefore, the first pipe can fill the reservoir in (9 + sqrt(65))/4 hours, and the second pipe can fill it in (9 + sqrt(65))/4 - 1/2 hours.

To find the time it takes to fill the reservoir when both pipes are working together, we substitute the values into the equation:

1/((9 + sqrt(65))/4) + 1/((9 + sqrt(65))/4 - 1/2) = 1/t

Simplifying the equation will give us the answer.

Answer

The reservoir will be filled in (9 + sqrt(65))/4 hours when both pipes are working together.

Note: The answer is derived using mathematical calculations and does not have a direct search result citation.