Question

4. Через первую трубу водоем можно наполнить за бч, а через вторую на 1 1/3 часа быстрее, чем первой. За сколько часов наполнится водоем при совместной работе этих труб? срочно пж​

Answer 1

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 2

Problem Analysis

We have two pipes, one of which can fill a pond in b hours, and the other can fill the same pond in (b - 1 1/3) hours. We need to find the time it takes to fill the pond when both pipes are working together.

Solution

Let's assume that the first pipe can fill the pond in b hours. This means that in one hour, the first pipe can fill 1/b of the pond.

The second pipe can fill the same pond in (b - 1 1/3) hours. This means that in one hour, the second pipe can fill 1/(b - 1 1/3) of the pond.

When both pipes are working together, the rate at which they fill the pond is the sum of their individual rates. So, the combined rate is:

1/b + 1/(b - 1 1/3)

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

Time = 1 / (1/b + 1/(b - 1 1/3))

Now, let's solve this equation to find the time it takes to fill the pond.

Calculation

Let's assume b = 4 (hours).

Substituting the value of b into the equation:

Time = 1 / (1/4 + 1/(4 - 1 1/3))

Simplifying the equation:

Time = 1 / (1/4 + 1/(10/3))

Time = 1 / (1/4 + 3/10)

Time = 1 / (10/40 + 12/40)

Time = 1 / (22/40)

Time = 40/22

Time ≈ 1.818 hours

Therefore, it will take approximately 1.818 hours to fill the pond when both pipes are working together.

Answer

The pond will be filled in approximately 1.818 hours when both pipes are working together.