Question

Через первую трубу водоём можно наполнить за 6 часов , а через вторую на 1 1/3 часа быстрее ,чем первая . За сколько часов наполнится водоём при совместной работы этих труб? Помогите Пожалуйста !!​

Answer 1

Ответ:

за 2 4/7 часа

Пошаговое объяснение:

Время, через которое, 2-я труба наполнит водоём:

6÷1 1/3=6·3/4=(3·3)/2=9/2 ч

За единицу примем сам водоём. Тогда:

1/6 - производительность 1-й трубы;

1/(9/2)=2/9 - производительность 2-й трубы.

Производительность двух труб:

1/6 +2/9=3/18 +4/18=7/18

Время, за которое наполнят две трубы водоём:

1/(7/18)=18/7=2 4/7 ч

Answer 2

Ответ:

за 2 5/8 часа две трубы наполнят водоём

Пошаговое объяснение:

По условию, через первую трубу водоем можно наполнить за 6 часов, а через вторую на 1 1/3 часа быстрее, чем первой.

6 - 1 1/3 = 4 2/3 часа потребуется второй трубе, чтобы наполнить водоём

Весь объём водоёма примем за 1 (одну целую) часть. Тогда:

1. 1 : 6 = 1/6 часть водоёма наполнит первая труба за 1 час

2. 1 : 4 2/3 = 1 : 14/3 = 1*3/14 = 3/14 части  водоёма наполнит вторая труба за 1 час

3. 1/6 + 3/14 = 7/42 + 9/42 = 16/42 = 8/21 части водоёма наполнят две трубы за 1 час

4. 1 : 8/21 = 1 * 21/8 = 21/8 = 2 5/8 часа потребуется двум трубам, чтобы наполнить водоём

Answer 3

Problem Analysis

We are given two pipes, one of which can fill a reservoir in 6 hours, and the other can fill it 1 1/3 hours faster 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 denote the time it takes to fill the reservoir using the first pipe as x hours. Since the second pipe is 1 1/3 hours faster, it will take x - 1 1/3 hours to fill the reservoir using the second pipe.

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 1/6 of the reservoir per hour, and the rate of the second pipe is 1/(x - 1 1/3) of the reservoir per hour.

To find the combined rate, we add the rates of the two pipes:

1/6 + 1/(x - 1 1/3)

To find the time it takes to fill the reservoir when both pipes are working together, we need to find the reciprocal of the combined rate:

1 / (1/6 + 1/(x - 1 1/3))

Let's simplify this expression to find the value of x.

Calculation

To simplify the expression, we need to find a common denominator for the two fractions in the denominator:

1 / (1/6 + 1/(x - 1 1/3)) = 1 / (1/6 + 3/(3x - 4))

Now, let's find the common denominator:

1 / (1/6 + 3/(3x - 4)) = 1 / (1/6 + (3 * 6) / (6 * (3x - 4)))

Simplifying further:

1 / (1/6 + (3 * 6) / (6 * (3x - 4))) = 1 / (1/6 + 18 / (6 * (3x - 4)))

1 / (1/6 + 18 / (6 * (3x - 4))) = 1 / (1/6 + 18 / (18x - 24))

Now, let's find the common denominator:

1 / (1/6 + 18 / (18x - 24)) = 1 / ((18x - 24 + 18) / (18x - 24))

Simplifying further:

1 / ((18x - 24 + 18) / (18x - 24)) = (18x - 24) / (18x - 24 + 18)

Now, we can simplify the expression:

(18x - 24) / (18x - 24 + 18) = (18x - 24) / (18x - 6)

So, the time it takes to fill the reservoir when both pipes are working together is given by:

x = (18x - 24) / (18x - 6)

To solve this equation, we can cross-multiply:

x * (18x - 6) = 18x - 24

Expanding the equation:

18x^2 - 6x = 18x - 24

Rearranging the terms:

18x^2 - 6x - 18x + 24 = 0

Combining like terms:

18x^2 - 24x + 24 = 0

Dividing all terms by 6:

3x^2 - 4x + 4 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -4, and c = 4. Substituting these values into the quadratic formula:

x = (-(-4) ± √((-4)^2 - 4 * 3 * 4)) / (2 * 3)

Simplifying:

x = (4 ± √(16 - 48)) / 6

x = (4 ± √(-32)) / 6

Since the discriminant is negative, the equation has no real solutions. This means that the given information is not consistent and there is no valid answer to the problem.

Conclusion

Based on the given information, it is not possible to determine the time it takes to fill the reservoir when both pipes are working together. The problem may contain conflicting or incorrect information.