Question

Только одному крану требуется на 4 часа больше времени, чтобы наполнить бассейн,чем другому крану. Если мы откроем оба одновременно, то бассейн будет заполнен через 4 часа 48 минут. За какое время каждый кран отдельно наполняет бассейн?​

Answer 1

Ответ:$\alpha$

Объяснение:

Answer 2

Problem Analysis

We are given two taps or faucets that fill a swimming pool. One tap takes 4 hours longer than the other tap to fill the pool. When both taps are opened simultaneously, the pool is filled in 4 hours and 48 minutes. We need to determine the time it takes for each tap to individually fill the pool.

Solution

Let's assume that the tap that takes less time to fill the pool is Tap A, and the tap that takes more time is Tap B.

Let's denote the time it takes for Tap A to fill the pool as x hours. Since Tap B takes 4 hours longer, it will take x + 4 hours to fill the pool.

When both taps are opened simultaneously, they fill the pool in 4 hours and 48 minutes, which is equivalent to 4.8 hours.

To find the individual times for each tap, we can set up the following equation based on the rates at which the taps fill the pool:

1/x + 1/(x + 4) = 1/4.8

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can multiply both sides by the least common multiple (LCM) of the denominators to eliminate the fractions.

LCM(1, 1) = 1

LCM(x, x + 4) = x(x + 4)

LCM(1/4.8) = 4.8

Multiplying both sides of the equation by the LCM, we get:

4.8(x(x + 4)) = x(x + 4)

Simplifying the equation:

4.8x^2 + 19.2x = x^2 + 4x

4.8x^2 + 19.2x - x^2 - 4x = 0

3.8x^2 + 15.2x = 0

Dividing both sides of the equation by x:

3.8x + 15.2 = 0

Solving for x:

3.8x = -15.2

x = -15.2 / 3.8

x = -4

Since time cannot be negative, we discard the negative solution.

Therefore, the time it takes for Tap A to fill the pool is x = 4 hours.

To find the time it takes for Tap B, we add 4 hours to Tap A's time:

4 + 4 = 8 hours

Therefore, Tap A takes 4 hours to fill the pool, and Tap B takes 8 hours to fill the pool.

Answer

Tap A takes 4 hours to fill the pool, and Tap B takes 8 hours to fill the pool.

Note: The negative solution obtained during the calculation is discarded as time cannot be negative.