Question

Бассейн наполняется через первую трубу за 4 часа, через вторую за 6 часов. Какую часть бассейна останется наполнить после совместной работы обеих труб в течении двух часов? ​

Answer 1

Половину останется заполнить наверное)

Answer 2

Ответ:

останется наполнить $\frac{1}{6}$ часть бассейна

Пошаговое объяснение:

1 труба за час наполняет 1/4

2 труба  за час наполняет 1/6

Тогда вместе за час работы наполнят:

$\frac{1}{4} +\frac{1}{6} =\frac{3}{12} +\frac{2}{12} =\frac{5}{12} \\\\\frac{5}{12} *2=\frac{10}{12} =\frac{5}{6}$

За 2 часа совместной работы наполнится 5/6 бассейна.

Вся работа равна 1,значит:

1= 6/6

6/6 - 5/6 = 1/6

Answer 3

#### Problem Analysis We are given two pipes, one that fills the pool in 4 hours and another that fills the pool in 6 hours. We need to determine the fraction of the pool that remains to be filled after both pipes have been working together for 2 hours. #### Solution To solve this problem, we can calculate the rate at which each pipe fills the pool and then determine the combined rate when both pipes are working together. Finally, we can calculate the fraction of the pool that remains to be filled after 2 hours. Let's calculate the rates at which each pipe fills the pool: - The first pipe fills the pool in 4 hours, so its rate is 1/4 of the pool per hour. - The second pipe fills the pool in 6 hours, so its rate is 1/6 of the pool per hour. To determine the combined rate when both pipes are working together, we can add their individual rates: - Combined rate = rate of first pipe + rate of second pipe Now, let's calculate the fraction of the pool that remains to be filled after 2 hours: - Fraction remaining = 1 - (combined rate * time) #### Calculation - Rate of first pipe = 1/4 of the pool per hour - Rate of second pipe = 1/6 of the pool per hour - Combined rate = (1/4) + (1/6) = 5/12 of the pool per hour - Time = 2 hours Now, let's calculate the fraction of the pool that remains to be filled after 2 hours: - Fraction remaining = 1 - (5/12 * 2) = 1 - (10/12) = 1 - (5/6) = 1/6 #### Answer After working together for 2 hours, **1/6** of the pool remains to be filled. #### Explanation When both pipes are working together, they fill a combined rate of 5/12 of the pool per hour. After 2 hours, they would have filled a total of (5/12 * 2) = 10/12 of the pool. Subtracting this from 1 gives us the fraction of the pool that remains to be filled, which is 1/6.