Question

Первой трубе, работая отдельно, требуется 4 часа для заполнения бассейна водой, а второй трубе – на 2 часа больше. Сначала включили только первую трубу, которая проработала 40 минут. Сколько необходимо времени, чтобы закончить заполнение бассейна, если теперь обе трубы будут работать вместе? Ответ запишите в часах.

Answer 1

  v        t        s
1/4      4        1 - 1 труба
1/6      6        1 - 2 труба
  v        t        s
1/4     2/3    1/6 - 1 труба работала 40 мин
5/12    x       5/6 - 2 трубы вместе

5/12x=5/6
x = 2часа
вроде так

Answer 2

Problem Analysis

We are given two pipes, and each pipe takes a different amount of time to fill a pool with water. The first pipe takes 4 hours, and the second pipe takes 2 hours longer than the first pipe. We are also told that the first pipe was turned on for 40 minutes before the second pipe was turned on. We need to determine how much time is needed to complete filling the pool when both pipes are working together.

Solution

To solve this problem, we can follow these steps: 1. Calculate the rate at which each pipe fills the pool. 2. Determine the amount of water filled by the first pipe in 40 minutes. 3. Calculate the remaining amount of water needed to fill the pool. 4. Calculate the time required to fill the remaining amount of water using both pipes.

Let's calculate the time required to fill the pool when both pipes are working together.

Step 1: Calculate the rate at which each pipe fills the pool

The first pipe takes 4 hours to fill the pool, which means it fills 1/4 of the pool in 1 hour. Therefore, the first pipe fills the pool at a rate of 1/4 pool per hour.

The second pipe takes 2 hours longer than the first pipe, so it takes 6 hours to fill the pool. This means it fills 1/6 of the pool in 1 hour. Therefore, the second pipe fills the pool at a rate of 1/6 pool per hour.

Step 2: Determine the amount of water filled by the first pipe in 40 minutes

Since the first pipe fills the pool at a rate of 1/4 pool per hour, we can calculate the amount of water filled by the first pipe in 40 minutes (2/3 of an hour) by multiplying the rate by the time:

Amount filled by the first pipe = (1/4) * (2/3) = 1/6 of the pool.

Step 3: Calculate the remaining amount of water needed to fill the pool

Since the first pipe filled 1/6 of the pool, the remaining amount of water needed to fill the pool is 1 - 1/6 = 5/6 of the pool.

Step 4: Calculate the time required to fill the remaining amount of water using both pipes

Now that we know the remaining amount of water needed to fill the pool is 5/6 of the pool, we can calculate the time required to fill this amount of water using both pipes.

Let's assume the time required to fill the remaining amount of water using both pipes is T hours.

The combined rate of both pipes is the sum of their individual rates:

Combined rate = (1/4 + 1/6) pool per hour.

Since the combined rate is the amount of water filled per hour, we can multiply it by T to get the amount of water filled in T hours:

Amount filled in T hours = (1/4 + 1/6) * T.

We know that the amount filled in T hours is equal to the remaining amount of water needed to fill the pool, which is 5/6 of the pool:

(1/4 + 1/6) * T = 5/6.

Now we can solve this equation to find the value of T.

Solving the equation

To solve the equation (1/4 + 1/6) * T = 5/6, we can simplify it by finding a common denominator for the fractions:

(3/12 + 2/12) * T = 5/6.

(5/12) * T = 5/6.

Now we can solve for T by multiplying both sides of the equation by the reciprocal of (5/12):

T = (5/6) * (12/5).

T = 2.4 hours.

Therefore, it will take 2.4 hours to complete filling the pool when both pipes are working together.

Answer

The time required to complete filling the pool when both pipes are working together is 2.4 hours.

Note

Please note that the given problem does not specify the size of the pool or the rate at which the pipes fill the pool. Therefore, we made assumptions based on the information provided.