Question

Через 1 трубу водоём можно наполнить за 9 часов, а через 2 трубу на 2 целых 1/3 часа быстрее, чем в первой. За сколько часов наполнится водоём при совместной работе? решите задачу с краткой записью, решением и ответом. дам 100 баллов

Answer 1

Пошаговое объяснение:

Целый водоём 1 труба = 9 часов

Целый водоём 2 труба = ? ч, на 2 1/3ч быстрее чем 1 труба

Целый водоём 1 труба + 2 труба = ? ч

1) 9 - 2 1/3 = 8 3/3 - 2 1/3 = 6 2/3 (часа) - наполнит весь водоём 2 труба работая в одиночку

2) 1 : 9 = 1/9 (часть) - всего водоёма заполняет за 1 час 1 труба

3) 1 : 6 2/3 = 1 : 20/3 = 1 * 3/20 = 3/20 (часть) - всего водоёма заполняет за 1 час 2 труба работая в одиночку

4) 1/9 + 3/20 = 20/180 + 27/180 = 47/180 (часть) - всего водоёма заполняют за 1 час две трубы работая вместе

5) 1 : 47/180 = 1 * 180/47 = 180/47 = 3 39/47 (часа) - заполнят весь водоём две трубы работая вместе

3 39/47 часа ≈ 3 часа 50 минут

Answer 2

Problem Analysis

We are given that one pipe can fill a reservoir in 9 hours, while another pipe can fill it in 2 hours and 1/3 less time 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 2 hours and 1/3 less time than the first pipe. This means the second pipe can fill the reservoir in (x - x/3) hours.

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

1 / (time taken by both pipes) = 1 / (time taken by first pipe) + 1 / (time taken by second pipe)

Let's solve this equation to find the time taken by both pipes.

Calculation

Let's substitute the values into the equation:

1 / (time taken by both pipes) = 1 / x + 1 / (x - x/3)

Simplifying the equation:

1 / (time taken by both pipes) = 1 / x + 1 / (2x/3)

To add the fractions, we need a common denominator:

1 / (time taken by both pipes) = (3 / 3x) + (3 / (2x))

Combining the fractions:

1 / (time taken by both pipes) = (6 + 9) / (6x)

Simplifying further:

1 / (time taken by both pipes) = 15 / (6x)

Now, let's invert both sides of the equation:

(time taken by both pipes) = (6x) / 15

Simplifying:

(time taken by both pipes) = 2x / 5

Therefore, the time taken to fill the reservoir when both pipes are working together is 2x / 5.

Answer

The reservoir will be filled in 2x / 5 hours when both pipes are working together.

Note: We need the value of x to calculate the exact time. Unfortunately, the given problem does not provide enough information to determine the value of x.