Question

4. Через первую трубу водоем можно наполнить за 8ч, а через вторую на 12 часа быстрее чем первой. 14 За сколько часов наполнится водоем при совместной работе этих труб в стиле чертижа пжж​

Answer 1

12+14*8 дальше сам.....

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a reservoir in 8 hours, and the other can fill the same reservoir in 12 hours less than the first pipe. We need to determine how long it will take to fill the reservoir when both pipes are used 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 12 hours less than the first pipe. Therefore, the second pipe can fill the reservoir in (x - 12) hours.

To find the time it takes to fill the reservoir when both pipes are used together, we can use the concept of work. The work done by each pipe is inversely proportional to the time it takes to complete the work. Therefore, the combined work done by both pipes is the sum of their individual work.

The work done by the first pipe in 1 hour is 1/x of the reservoir, and the work done by the second pipe in 1 hour is 1/(x - 12) of the reservoir. Therefore, the combined work done by both pipes in 1 hour is:

1/x + 1/(x - 12)

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

1/x + 1/(x - 12) = 1/t

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

Now, we can solve this equation to find the value of t.

Calculation

Let's solve the equation 1/x + 1/(x - 12) = 1/t to find the value of t.

1/x + 1/(x - 12) = 1/t

To simplify the equation, we can multiply both sides by x(x - 12)t:

t(x - 12) + tx = x(x - 12)

Expanding the equation:

tx - 12t + tx = x^2 - 12x

Combining like terms:

2tx - 12t = x^2 - 12x

Moving all terms to one side:

x^2 - (2tx - 12t) - 12x = 0

Rearranging the terms:

x^2 - 12x - 2tx + 12t = 0

Factoring out x:

x(x - 12) - 2t(x - 12) = 0

(x - 2t)(x - 12) = 0

Setting each factor equal to zero:

x - 2t = 0 or x - 12 = 0

Solving for x:

x = 2t or x = 12

Since x represents the time it takes for the first pipe to fill the reservoir, it cannot be 12 hours (as the second pipe fills the reservoir in x - 12 hours). Therefore, x must be equal to 2t.

Substituting x = 2t into the equation 1/x + 1/(x - 12) = 1/t:

1/(2t) + 1/(2t - 12) = 1/t

Multiplying both sides by 2t(2t - 12):

2t - 12 + 2t = 2(2t - 12)

4t - 12 = 4t - 24

Subtracting 4t from both sides:

-12 = -24

This equation is not possible, as -12 is not equal to -24. Therefore, there is no solution to the equation.

Conclusion

Based on the given information, it is not possible to determine the time it takes to fill the reservoir when both pipes are used together.