Question

Две трубы,работая совместно,наполняют бассейн за 6 часов. Первая труба наполняет на 50% больше в час чем вторая. За сколько часов каждая труба сможет отдельно наполнить бассейн?

Answer 1

Возьмем производительность первой x и второй у.
(x+y)*6=1
x=1.5y
Значит (1,5у+у)*6=1
15у=1
у=1/15
1/15*t=1
t=15 часов. 
x=$\frac{1.5}{15} = 0.1$
x*t=1
t=10 часов. 
Ответ: первая труба за 10ч, вторая за 15ч.

Answer 2

Problem Analysis

We are given that two pipes, working together, can fill a pool in 6 hours. The first pipe fills the pool at a rate that is 50% faster than the second pipe. We need to determine how long it would take for each pipe to fill the pool individually.

Solution

Let's assume that the second pipe fills the pool in x hours. Since the first pipe fills the pool 50% faster, it would take 0.5x hours less than the second pipe to fill the pool.

To find the individual rates of each pipe, we can use the formula: rate = work / time.

Let's calculate the rates of the two pipes working together and set up an equation based on the given information:

The combined rate of the two pipes working together is 1 pool per 6 hours, so the equation is: 1/6 = 1/x + 1/(x - 0.5x).

Simplifying the equation: 1/6 = 1/x + 1/(0.5x).

To solve this equation, we can find a common denominator and combine the fractions: 1/6 = (2 + 4)/(2x).

Simplifying further: 1/6 = 6/(2x).

Cross-multiplying: 6 * 2x = 6 * 6.

Simplifying: 12x = 36.

Dividing both sides by 12: x = 3.

Therefore, the second pipe can fill the pool on its own in 3 hours. Since the first pipe fills the pool 50% faster, it would take 2.5 hours to fill the pool individually.

Answer

The second pipe can fill the pool on its own in 3 hours, while the first pipe can fill the pool on its own in 2.5 hours.