Question

Плавательный бассейн наполняется двумя трубами при совместной их работе за 48 мин. Через первую трубу он может наполниться за 2 ч. За сколько времени наполнится бассейн н 3|4 своего объема только через одну вторую трубу?

Answer 1

Система:
(x+y)*4/5=1
x*2=1
Решение x = 1/2, y = 3/4.
y*t=3/4
t = 1.
Ответ: 1 час.

Answer 2

Problem Analysis

We are given that a swimming pool is being filled by two pipes working together, and it takes 48 minutes to fill the pool. We also know that the first pipe can fill the pool in 2 hours. We need to determine how long it will take to fill 3/4 of the pool's volume using only the second pipe.

Solution

Let's assume that the volume of the pool is represented by V. We are trying to find the time it takes to fill 3/4 of the pool's volume using only the second pipe.

We can start by finding the rate at which the first pipe fills the pool. Since the first pipe can fill the pool in 2 hours, its rate of filling the pool is 1/2 of the pool's volume per hour.

Next, we can find the rate at which both pipes fill the pool. We are given that both pipes together can fill the pool in 48 minutes, which is equivalent to 48/60 = 4/5 hours. Therefore, the rate at which both pipes fill the pool is (1 pool volume) / (4/5 hours) = 5/4 of the pool's volume per hour.

Now, let's find the rate at which the second pipe fills the pool. We can subtract the rate of the first pipe from the rate of both pipes together. This gives us (5/4 - 1/2) = 3/4 of the pool's volume per hour.

Since we want to find the time it takes to fill 3/4 of the pool's volume using only the second pipe, we can set up the following equation:

(3/4)V = (3/4 of the pool's volume) / (time taken by the second pipe)

Simplifying the equation, we find:

(time taken by the second pipe) = (3/4 of the pool's volume) / ((3/4)V)

The volume of the pool cancels out, leaving us with:

(time taken by the second pipe) = 1 / (3/4)

Simplifying further, we find:

(time taken by the second pipe) = 4/3 hours

Converting this to minutes, we have:

(time taken by the second pipe) = (4/3) * 60 = 80 minutes

Therefore, it will take 80 minutes for the pool to be filled with 3/4 of its volume using only the second pipe.

Answer

The swimming pool will be filled with 3/4 of its volume using only the second pipe in 80 minutes.