Question

Через первую трубу водоем можно наполнить за 6ч, а через вторую на 1 1/3 часа быстрее, чем первой. За сколько часов наполнится водоем при совместной работе этих труб? краткую запись, плиз!!!​

Answer 1

Ответ:

за 2 4/7 ч.

Пошаговое объяснение:

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

6:1 1/3=6*3/4=(3*3)/2=9/2 ч.

За единицу примем сам водоем. Тогда:

1/6-производительность 1 трубы;

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

Производительность двух труб:

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

Время, за которое наполнят две трубы водоем:

1/(7/18)=18/7=2 4/7

Ответ: 2 4/7

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a reservoir in 6 hours, and the other can fill the reservoir 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 for the first pipe to fill the reservoir as x hours. According to the problem, the second pipe can fill the reservoir 1 1/3 hours faster than the first pipe. Therefore, the second pipe can fill the reservoir in x - 1 1/3 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 the first pipe) + 1 / (time taken by the second pipe) = 1 / (time taken when both pipes are working together)

Substituting the values, we get:

1 / x + 1 / (x - 1 1/3) = 1 / (time taken when both pipes are working together)

To solve this equation, we can find a common denominator and simplify:

[(x - 1 1/3) + x] / [x(x - 1 1/3)] = 1 / (time taken when both pipes are working together)

Simplifying further:

[2x - 1 1/3] / [x(x - 1 1/3)] = 1 / (time taken when both pipes are working together)

Now, we can cross-multiply to solve for the time taken when both pipes are working together:

[x(x - 1 1/3)] = [2x - 1 1/3]

Simplifying further:

x^2 - (4/3)x + 4/9 = 2x - 1 1/3

Converting the mixed number to an improper fraction:

x^2 - (4/3)x + 4/9 = 2x - 4/3

Combining like terms:

x^2 - (4/3)x - 2x + 4/9 + 4/3 = 0

Simplifying further:

x^2 - (10/3)x + 16/9 = 0

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