Question

Одна труба наполняет бассейн за 12 часов ; вторая труба - за 15 часов. за сколько часов наполнят бассейн обе трубы одновременно ?

Answer 1

12+15=27(ч)-наполнят бассейн обе трубы.

Answer 2

Problem Analysis

We are given two pipes that fill a pool. The first pipe fills the pool in 12 hours, and the second pipe fills the pool in 15 hours. We need to determine how long it will take for both pipes to fill the pool simultaneously.

Solution

To solve this problem, we can use the concept of rates. The rate at which the first pipe fills the pool is 1/12 of the pool per hour, and the rate at which the second pipe fills the pool is 1/15 of the pool per hour. When both pipes are working together, their combined rate is the sum of their individual rates.

Let's assume that it takes x hours for both pipes to fill the pool together. During this time, the first pipe will fill x/12 of the pool, and the second pipe will fill x/15 of the pool. Since they are working together, the sum of these amounts should equal the entire pool.

Mathematically, we can express this as:

x/12 + x/15 = 1

To solve this equation, we can find a common denominator and then combine the fractions:

(15x + 12x) / (12 * 15) = 1

27x / 180 = 1

Now, we can solve for x by multiplying both sides of the equation by 180/27:

x = (180/27) * 1

Simplifying the expression:

x = 6.67 hours

Therefore, it will take approximately 6.67 hours for both pipes to fill the pool simultaneously.

Answer

Both pipes will fill the pool simultaneously in approximately 6.67 hours.