Question

4. Через первую трубу водоем можно наполнить за 8ч, а через вторую на 1 часа быстрее, чем первой. За сколько часов наполнится водоем при совместной работе этих труб?​

Answer 1

Ответ:

3 часа 44 минуты

Пошаговое объяснение:

1) 8 - 1 = 7 (часов) - можно заполнить водоём 2 трубой

2) 1 : 8 = 1/8 (часть) - всего водоема заполняет за 1 час 1 труба

3) 1 : 7 = 1/7 (часть) - всего водоёма заполняет за 1 час 2 труба

4) 1/8 + 1/7 = 7/56 + 8/56 = 15/56 (часть) - всего водоёма заполняют за 1 час две трубы работая вместе

5) 1 : 15/56 = 1 * 56/15 = 56/15 = 3 11/15 (часа) - наполнят весь водоём две трубы работая вместе

1 час = 60 минут

3 11/15 часа = 3ч + 11/15ч = 3ч + 60 * 11/15 = 3ч + 660/15 = 3ч + 44мин = 3часа 44 минуты

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a reservoir in 8 hours, and the other can fill it in 1 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 hour less than the first pipe. Therefore, the second pipe can fill the reservoir in (x - 1) hours.

To find the time it takes to fill the reservoir when both pipes are working together, we can use the formula:

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

Where: - x is the time taken by the first pipe to fill the reservoir alone. - (x - 1) is the time taken by the second pipe to fill the reservoir alone. - t is the time taken to fill the reservoir when both pipes are working together.

To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators to eliminate the fractions.

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

Simplifying the equation:

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

Cross-multiplying:

(2x - 1) * t = x * (x - 1)

Expanding:

2xt - t = x^2 - x

Rearranging the equation:

x^2 - 2xt + x - t = 0

This is a quadratic equation. We can solve it to find the value of x, which represents the time taken by the first pipe to fill the reservoir alone.

Once we find the value of x, we can substitute it back into the equation to find the value of t, which represents the time taken to fill the reservoir when both pipes are working together.

Let's solve the equation to find the values of x and t.

Solution Steps:

1. Set up the equation: x^2 - 2xt + x - t = 0 2. Solve the equation for x using factoring, completing the square, or the quadratic formula. 3. Substitute the value of x back into the equation to find the value of t.

Solution

Let's solve the equation to find the values of x and t.

1. Set up the equation: x^2 - 2xt + x - t = 0 2. Rearrange the equation: x^2 - 2xt + x - t = 0 3. Combine like terms: x^2 + x - 2xt - t = 0 4. Factor by grouping: x(x + 1) - t(2x + 1) = 0 5. Factor out x from the first two terms and -t from the last two terms: x(x + 1) - t(2x + 1) = 0 6. Apply the zero-product property: x = 0 or x + 1 = 0 or 2x + 1 = 0 7. Solve for x: - If x = 0, then the first pipe cannot fill the reservoir, which is not possible. - If x + 1 = 0, then x = -1, which is not a valid solution since time cannot be negative. - If 2x + 1 = 0, then 2x = -1, and x = -1/2. 8. Substitute the value of x back into the equation to find the value of t: - If x = -1/2, then t = (-1/2)(-1/2 + 1) = (-1/2)(1/2) = -1/4. - Since time cannot be negative, the value of t is not valid. 9. Therefore, there is no valid solution for this problem.

Based on the given information, it seems that there is an error or inconsistency in the problem statement. Please double-check the problem or provide additional information if available.

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